Page 1 [1] (Waves & Oscillations) 1. A particle of mass m g is executing S.H. M. about a point with amplitude 10- cm. Its maximum velocity is 100 cms –1 . Its velocity will be 50 cms –1 at a distance (a) 5 cm (b) 5 2 cm (c) 3 5 cm (d) 2 10 cm 2. A S.H.M. oscillator has period of 0.1 sec and amplitude of 0.2 m. The maximum velocity is given by (a) 100 ms –1 (b) 4 p ms –1 (c) 100 p ms –1 (d) 20 p ms –1 3. If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone (a) reaches the centre of earth and stops (b) reaches the opposite end and stops (c) executes S.H.M. about the centre of earth (d) reaches the opposite side and escapes earth 4. Total energy of the particles executing S.H. M is proportional to (a) displacement of the particle (b) frequency of oscillation (c) square of the amplitude (d) velocity at the mean position 5. A pendulum suspended to the celling of a train has a period T when the train is at rest. If the train is accelerated uniformly, the period will (a) Increase (b) decrease (c) remain the same (d) become infinite 6. A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6 th of that on earth. Its period will be (a) 6 T (b) 3 T (c) 3 T (d) 6 T 7. The angular frequency of a pendulum is ? rad s –1 . If the length is made one fourth of the orginal length, the angular frequency becomes (a) 2 ? (b) 2 ? (c) 4 ? (d) ?/4 8. A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period (a) remains the same (b) decreases (c) increases (d) no vibration is possible 9. A particle moves such that its motion is represented by a = kx, where ‘a’ is the acceleration and x is displacement and k is a constant. The period of oscillation is (a) 2 p k (b) k 2 p (c) k 2 p (d) none of these 10. A simple pendulum consists of a bob of radius r and mass m and its period is 2 sec. When its bob is replaced by a bob of mass 2m but same radius r, the time period of motion is (a) 4 sec (b) 2 sec (c) 6 sec (d) 8 sec 11. A simple pendulum has a period T inside a lift when it is stationary. The lift is accelerated upwards with constant acceleration ‘a’ . The period (a) decreases (b) increases (c) remains same (d) sometimes increases and sometimes decreases 12. In above question if lift is accelerated downwards with constant acceleration, the period (a) decreases b) increases (c) remains same (d) none 13. The angular velocities of three bodies in simple harmonic motion are ? 1 , ? 2 , ? 3 with their respective amplitude as A 1 , A 2 , A 3 . If all the three bodies have same mass and maximum velocity, then : (a) A 2 1 ? 2 1 = A 2 2 ? 2 2 = A 2 3 ? 2 3 (b) A 2 1 ? 1 = A 2 2 ? 2 = A 2 3 ? 3 (c) A 1 ? 2 1 = A 2 ? 2 2 = A 3 ? 2 3 (d) A 1 ? 1 = A 2 ? 2 = A 3 ? 3 14. In arrangement shown in Fig., if the block of mass ‘m’ is displaced and then released the frequency of oscillation is given by : Page 2 [1] (Waves & Oscillations) 1. A particle of mass m g is executing S.H. M. about a point with amplitude 10- cm. Its maximum velocity is 100 cms –1 . Its velocity will be 50 cms –1 at a distance (a) 5 cm (b) 5 2 cm (c) 3 5 cm (d) 2 10 cm 2. A S.H.M. oscillator has period of 0.1 sec and amplitude of 0.2 m. The maximum velocity is given by (a) 100 ms –1 (b) 4 p ms –1 (c) 100 p ms –1 (d) 20 p ms –1 3. If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone (a) reaches the centre of earth and stops (b) reaches the opposite end and stops (c) executes S.H.M. about the centre of earth (d) reaches the opposite side and escapes earth 4. Total energy of the particles executing S.H. M is proportional to (a) displacement of the particle (b) frequency of oscillation (c) square of the amplitude (d) velocity at the mean position 5. A pendulum suspended to the celling of a train has a period T when the train is at rest. If the train is accelerated uniformly, the period will (a) Increase (b) decrease (c) remain the same (d) become infinite 6. A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6 th of that on earth. Its period will be (a) 6 T (b) 3 T (c) 3 T (d) 6 T 7. The angular frequency of a pendulum is ? rad s –1 . If the length is made one fourth of the orginal length, the angular frequency becomes (a) 2 ? (b) 2 ? (c) 4 ? (d) ?/4 8. A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period (a) remains the same (b) decreases (c) increases (d) no vibration is possible 9. A particle moves such that its motion is represented by a = kx, where ‘a’ is the acceleration and x is displacement and k is a constant. The period of oscillation is (a) 2 p k (b) k 2 p (c) k 2 p (d) none of these 10. A simple pendulum consists of a bob of radius r and mass m and its period is 2 sec. When its bob is replaced by a bob of mass 2m but same radius r, the time period of motion is (a) 4 sec (b) 2 sec (c) 6 sec (d) 8 sec 11. A simple pendulum has a period T inside a lift when it is stationary. The lift is accelerated upwards with constant acceleration ‘a’ . The period (a) decreases (b) increases (c) remains same (d) sometimes increases and sometimes decreases 12. In above question if lift is accelerated downwards with constant acceleration, the period (a) decreases b) increases (c) remains same (d) none 13. The angular velocities of three bodies in simple harmonic motion are ? 1 , ? 2 , ? 3 with their respective amplitude as A 1 , A 2 , A 3 . If all the three bodies have same mass and maximum velocity, then : (a) A 2 1 ? 2 1 = A 2 2 ? 2 2 = A 2 3 ? 2 3 (b) A 2 1 ? 1 = A 2 2 ? 2 = A 2 3 ? 3 (c) A 1 ? 2 1 = A 2 ? 2 2 = A 3 ? 2 3 (d) A 1 ? 1 = A 2 ? 2 = A 3 ? 3 14. In arrangement shown in Fig., if the block of mass ‘m’ is displaced and then released the frequency of oscillation is given by : [2] (a) v = m k k 2 1 2 1 - p (b) v = m k k 2 1 2 1 + p (c) v = 2 1 k k m 2 1 - p (d) v = 2 1 k k m 2 1 + p 15. A pendulum bob has a period 24 s. Its velocity 4 sec after it has passed the mean position is 6.28 cm s - 1 . The amplitude of its motion is : (a) 12 cm (b) 24 cm (c) 48 cm (d) 40 cm 16. The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is : (a) 10 log (2) (b) 20 log (3) (c) 10 log (3) (d) 10 log (2) 17. A motorcyclist is moving towards a stationary car which is emitting a sound of 165 Hz, and a police car is chasing the motorcyclist blowing siren at frequency 172 Hz. If speed of police car is 22 m/s, then the speed of motorcyclist for which the motorcyclist hears no beats is : (a) 33 m/s (b) 22 m/s (c) 11 m/s (d) zero 18. The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y = 4 sin ( px/15) cos (96 pt), where x and y are in cm and t in seconds. The maximum displacement at x = 5 cm is : (a) 2 3 cm (b) 3 2 cm (c) 2 cm (d) 3 cm 19. In the above question, the nodes are located along the string at : (a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60 (c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 20. For production of beats the two sources must have : (a) different frequencies and same amplitude (b) different frequencies (c) different frequencies, same amplitude and same phase (d) different frequencies and same phase 21. The displacement versus time graph of SHM is given below : Which of the following is its acceleration versus time graph ? 22. Velocity of sound in a gas is proportional to : (a) square root of isothermal elasticity (b) adiabatic elasticity (c) square root of adiabatic elasticity (d) isothermal elasticity 23. Mechanical wave (sound wave) in a gas is : (a) transverse (b) longitudinal (c) neither transverse nor longitudinal (d) either transverse dependent 24. A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) : (a) T/2 (b) T/4 (c) T (d) 2T 25. The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency : (a) 10 Hz (b) 360 Hz (c) 216 Hz (d) 6 Hz In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: Page 3 [1] (Waves & Oscillations) 1. A particle of mass m g is executing S.H. M. about a point with amplitude 10- cm. Its maximum velocity is 100 cms –1 . Its velocity will be 50 cms –1 at a distance (a) 5 cm (b) 5 2 cm (c) 3 5 cm (d) 2 10 cm 2. A S.H.M. oscillator has period of 0.1 sec and amplitude of 0.2 m. The maximum velocity is given by (a) 100 ms –1 (b) 4 p ms –1 (c) 100 p ms –1 (d) 20 p ms –1 3. If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone (a) reaches the centre of earth and stops (b) reaches the opposite end and stops (c) executes S.H.M. about the centre of earth (d) reaches the opposite side and escapes earth 4. Total energy of the particles executing S.H. M is proportional to (a) displacement of the particle (b) frequency of oscillation (c) square of the amplitude (d) velocity at the mean position 5. A pendulum suspended to the celling of a train has a period T when the train is at rest. If the train is accelerated uniformly, the period will (a) Increase (b) decrease (c) remain the same (d) become infinite 6. A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6 th of that on earth. Its period will be (a) 6 T (b) 3 T (c) 3 T (d) 6 T 7. The angular frequency of a pendulum is ? rad s –1 . If the length is made one fourth of the orginal length, the angular frequency becomes (a) 2 ? (b) 2 ? (c) 4 ? (d) ?/4 8. A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period (a) remains the same (b) decreases (c) increases (d) no vibration is possible 9. A particle moves such that its motion is represented by a = kx, where ‘a’ is the acceleration and x is displacement and k is a constant. The period of oscillation is (a) 2 p k (b) k 2 p (c) k 2 p (d) none of these 10. A simple pendulum consists of a bob of radius r and mass m and its period is 2 sec. When its bob is replaced by a bob of mass 2m but same radius r, the time period of motion is (a) 4 sec (b) 2 sec (c) 6 sec (d) 8 sec 11. A simple pendulum has a period T inside a lift when it is stationary. The lift is accelerated upwards with constant acceleration ‘a’ . The period (a) decreases (b) increases (c) remains same (d) sometimes increases and sometimes decreases 12. In above question if lift is accelerated downwards with constant acceleration, the period (a) decreases b) increases (c) remains same (d) none 13. The angular velocities of three bodies in simple harmonic motion are ? 1 , ? 2 , ? 3 with their respective amplitude as A 1 , A 2 , A 3 . If all the three bodies have same mass and maximum velocity, then : (a) A 2 1 ? 2 1 = A 2 2 ? 2 2 = A 2 3 ? 2 3 (b) A 2 1 ? 1 = A 2 2 ? 2 = A 2 3 ? 3 (c) A 1 ? 2 1 = A 2 ? 2 2 = A 3 ? 2 3 (d) A 1 ? 1 = A 2 ? 2 = A 3 ? 3 14. In arrangement shown in Fig., if the block of mass ‘m’ is displaced and then released the frequency of oscillation is given by : [2] (a) v = m k k 2 1 2 1 - p (b) v = m k k 2 1 2 1 + p (c) v = 2 1 k k m 2 1 - p (d) v = 2 1 k k m 2 1 + p 15. A pendulum bob has a period 24 s. Its velocity 4 sec after it has passed the mean position is 6.28 cm s - 1 . The amplitude of its motion is : (a) 12 cm (b) 24 cm (c) 48 cm (d) 40 cm 16. The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is : (a) 10 log (2) (b) 20 log (3) (c) 10 log (3) (d) 10 log (2) 17. A motorcyclist is moving towards a stationary car which is emitting a sound of 165 Hz, and a police car is chasing the motorcyclist blowing siren at frequency 172 Hz. If speed of police car is 22 m/s, then the speed of motorcyclist for which the motorcyclist hears no beats is : (a) 33 m/s (b) 22 m/s (c) 11 m/s (d) zero 18. The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y = 4 sin ( px/15) cos (96 pt), where x and y are in cm and t in seconds. The maximum displacement at x = 5 cm is : (a) 2 3 cm (b) 3 2 cm (c) 2 cm (d) 3 cm 19. In the above question, the nodes are located along the string at : (a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60 (c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 20. For production of beats the two sources must have : (a) different frequencies and same amplitude (b) different frequencies (c) different frequencies, same amplitude and same phase (d) different frequencies and same phase 21. The displacement versus time graph of SHM is given below : Which of the following is its acceleration versus time graph ? 22. Velocity of sound in a gas is proportional to : (a) square root of isothermal elasticity (b) adiabatic elasticity (c) square root of adiabatic elasticity (d) isothermal elasticity 23. Mechanical wave (sound wave) in a gas is : (a) transverse (b) longitudinal (c) neither transverse nor longitudinal (d) either transverse dependent 24. A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) : (a) T/2 (b) T/4 (c) T (d) 2T 25. The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency : (a) 10 Hz (b) 360 Hz (c) 216 Hz (d) 6 Hz In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: [3] (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: Sound travels slower on a rainy day than on a dry day Reason: Moisture decreases the pressure 27. Assertion: The coefficient of adiabatic elasticity is smaller than the coefficient of isothermal elasticity. Reason: Heat is exchanged freely in an adiabatic change but not in an isothermal change. 28. Assertion: The amplitude of an oscillating pendulum decreases gradually with time. Reason: The frequency of the pendulum decreases with time. 29. Assertion: The time period of a simple pendulum inside a lift falling freely is zero. Reason: A body falling freely has infinite acceleration. 30. Assertion: When a spring is cut into 4 equal parts, the force constant becomes 4 times Reason: When two springs of spring constant k 1 and k 2 are connected in parallel, the force constant of combination become k 1 + k 2 . Test- 05 (Waves & Oscillations) ANSWERS 1 C 6 D 11 A 16 B 21 B 26 D 2 B 7 B 12 B 17 B 22 C 27 D 3 C 8 B 13 D 18 A 23 B 28 C 4 C 9 B 14 B 19 A 24 B 29 D 5 B 10 B 15 C 20 C 25 B 30 B SOLUTIONS 1. v max = r ? ? 100 = 10. ? ? ? = 10 rad/s Now v 2 = ? 2 (r 2 - y 2 ) ? 2500 = 100 (100 - y 2 ) y 2 = 100 - 25 = 75 y = 5 3 cm 2. w = T 2 p and v max = r ?, v max = 0.2 × 1 . 0 2 p = 4 p m/s 3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional to displacement from mean position is directed towards centre of earth. At depth d, g’ ? ? ? ? ? ? - R d 1 , = g ? ? ? ? ? ? - R d R 4. E = 2 1 mr 2 ? 2 ? E ? r 2 5. When train accelerates, then net acceleration is a’ = 2 2 a g + ? a’ > g ? T ? on accelerati 1 ? Time period decreases 6. 2 1 1 2 a a T T = ? T 2 = T 6 T 6 / g g = 7. ? = 2 pv = 2 p × p 2 1 l g = l g ? ?’ = l g 2 l g 4 4 l g = = ? ?’ = 2 ? 8. Due to attractive force of electrostatic field of positive charge, time period will decreases. Page 4 [1] (Waves & Oscillations) 1. A particle of mass m g is executing S.H. M. about a point with amplitude 10- cm. Its maximum velocity is 100 cms –1 . Its velocity will be 50 cms –1 at a distance (a) 5 cm (b) 5 2 cm (c) 3 5 cm (d) 2 10 cm 2. A S.H.M. oscillator has period of 0.1 sec and amplitude of 0.2 m. The maximum velocity is given by (a) 100 ms –1 (b) 4 p ms –1 (c) 100 p ms –1 (d) 20 p ms –1 3. If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone (a) reaches the centre of earth and stops (b) reaches the opposite end and stops (c) executes S.H.M. about the centre of earth (d) reaches the opposite side and escapes earth 4. Total energy of the particles executing S.H. M is proportional to (a) displacement of the particle (b) frequency of oscillation (c) square of the amplitude (d) velocity at the mean position 5. A pendulum suspended to the celling of a train has a period T when the train is at rest. If the train is accelerated uniformly, the period will (a) Increase (b) decrease (c) remain the same (d) become infinite 6. A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6 th of that on earth. Its period will be (a) 6 T (b) 3 T (c) 3 T (d) 6 T 7. The angular frequency of a pendulum is ? rad s –1 . If the length is made one fourth of the orginal length, the angular frequency becomes (a) 2 ? (b) 2 ? (c) 4 ? (d) ?/4 8. A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period (a) remains the same (b) decreases (c) increases (d) no vibration is possible 9. A particle moves such that its motion is represented by a = kx, where ‘a’ is the acceleration and x is displacement and k is a constant. The period of oscillation is (a) 2 p k (b) k 2 p (c) k 2 p (d) none of these 10. A simple pendulum consists of a bob of radius r and mass m and its period is 2 sec. When its bob is replaced by a bob of mass 2m but same radius r, the time period of motion is (a) 4 sec (b) 2 sec (c) 6 sec (d) 8 sec 11. A simple pendulum has a period T inside a lift when it is stationary. The lift is accelerated upwards with constant acceleration ‘a’ . The period (a) decreases (b) increases (c) remains same (d) sometimes increases and sometimes decreases 12. In above question if lift is accelerated downwards with constant acceleration, the period (a) decreases b) increases (c) remains same (d) none 13. The angular velocities of three bodies in simple harmonic motion are ? 1 , ? 2 , ? 3 with their respective amplitude as A 1 , A 2 , A 3 . If all the three bodies have same mass and maximum velocity, then : (a) A 2 1 ? 2 1 = A 2 2 ? 2 2 = A 2 3 ? 2 3 (b) A 2 1 ? 1 = A 2 2 ? 2 = A 2 3 ? 3 (c) A 1 ? 2 1 = A 2 ? 2 2 = A 3 ? 2 3 (d) A 1 ? 1 = A 2 ? 2 = A 3 ? 3 14. In arrangement shown in Fig., if the block of mass ‘m’ is displaced and then released the frequency of oscillation is given by : [2] (a) v = m k k 2 1 2 1 - p (b) v = m k k 2 1 2 1 + p (c) v = 2 1 k k m 2 1 - p (d) v = 2 1 k k m 2 1 + p 15. A pendulum bob has a period 24 s. Its velocity 4 sec after it has passed the mean position is 6.28 cm s - 1 . The amplitude of its motion is : (a) 12 cm (b) 24 cm (c) 48 cm (d) 40 cm 16. The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is : (a) 10 log (2) (b) 20 log (3) (c) 10 log (3) (d) 10 log (2) 17. A motorcyclist is moving towards a stationary car which is emitting a sound of 165 Hz, and a police car is chasing the motorcyclist blowing siren at frequency 172 Hz. If speed of police car is 22 m/s, then the speed of motorcyclist for which the motorcyclist hears no beats is : (a) 33 m/s (b) 22 m/s (c) 11 m/s (d) zero 18. The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y = 4 sin ( px/15) cos (96 pt), where x and y are in cm and t in seconds. The maximum displacement at x = 5 cm is : (a) 2 3 cm (b) 3 2 cm (c) 2 cm (d) 3 cm 19. In the above question, the nodes are located along the string at : (a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60 (c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 20. For production of beats the two sources must have : (a) different frequencies and same amplitude (b) different frequencies (c) different frequencies, same amplitude and same phase (d) different frequencies and same phase 21. The displacement versus time graph of SHM is given below : Which of the following is its acceleration versus time graph ? 22. Velocity of sound in a gas is proportional to : (a) square root of isothermal elasticity (b) adiabatic elasticity (c) square root of adiabatic elasticity (d) isothermal elasticity 23. Mechanical wave (sound wave) in a gas is : (a) transverse (b) longitudinal (c) neither transverse nor longitudinal (d) either transverse dependent 24. A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) : (a) T/2 (b) T/4 (c) T (d) 2T 25. The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency : (a) 10 Hz (b) 360 Hz (c) 216 Hz (d) 6 Hz In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: [3] (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: Sound travels slower on a rainy day than on a dry day Reason: Moisture decreases the pressure 27. Assertion: The coefficient of adiabatic elasticity is smaller than the coefficient of isothermal elasticity. Reason: Heat is exchanged freely in an adiabatic change but not in an isothermal change. 28. Assertion: The amplitude of an oscillating pendulum decreases gradually with time. Reason: The frequency of the pendulum decreases with time. 29. Assertion: The time period of a simple pendulum inside a lift falling freely is zero. Reason: A body falling freely has infinite acceleration. 30. Assertion: When a spring is cut into 4 equal parts, the force constant becomes 4 times Reason: When two springs of spring constant k 1 and k 2 are connected in parallel, the force constant of combination become k 1 + k 2 . Test- 05 (Waves & Oscillations) ANSWERS 1 C 6 D 11 A 16 B 21 B 26 D 2 B 7 B 12 B 17 B 22 C 27 D 3 C 8 B 13 D 18 A 23 B 28 C 4 C 9 B 14 B 19 A 24 B 29 D 5 B 10 B 15 C 20 C 25 B 30 B SOLUTIONS 1. v max = r ? ? 100 = 10. ? ? ? = 10 rad/s Now v 2 = ? 2 (r 2 - y 2 ) ? 2500 = 100 (100 - y 2 ) y 2 = 100 - 25 = 75 y = 5 3 cm 2. w = T 2 p and v max = r ?, v max = 0.2 × 1 . 0 2 p = 4 p m/s 3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional to displacement from mean position is directed towards centre of earth. At depth d, g’ ? ? ? ? ? ? - R d 1 , = g ? ? ? ? ? ? - R d R 4. E = 2 1 mr 2 ? 2 ? E ? r 2 5. When train accelerates, then net acceleration is a’ = 2 2 a g + ? a’ > g ? T ? on accelerati 1 ? Time period decreases 6. 2 1 1 2 a a T T = ? T 2 = T 6 T 6 / g g = 7. ? = 2 pv = 2 p × p 2 1 l g = l g ? ?’ = l g 2 l g 4 4 l g = = ? ?’ = 2 ? 8. Due to attractive force of electrostatic field of positive charge, time period will decreases. [4] 9. Time period of S.H.M. is T = 2 p on accelerati nt displaceme ? T = 2 p kx x ? T = k 2 p 10. Time period is independent of mass of bob so long as length remains constant. 11. When the lift ascends with acceleration a then apparent value of acceleration due to gravity becomes (g + a) As T = 2 p g ? . So the time period decreases. 12. During downward motion apparent value of g becomes (g - a). As T ? g 1 ? Time period increases 13. The general equation for a body executing simple harmonic motion is given by : y = A sin ?t. Velocity is given by : ? = dt d dt dy = (A sin ?t) = A ? cos ?t. For maximum velocity, we put cos ?t = 1 Hence, ? max. = A ? Now, since the velocities of three bodies are same, therefore we have : ? 1 = ? 2 = ? 3 A 1 ? 1 = A 2 ? 2 = A 2 ? 3 14. In this case springs are in parallel. ? k p = k 1 + k 2 ? T = 2 p 2 1 k k m + = ? = m k k 2 1 2 1 + p 15. Use v = r ? cos ?t, 6.28 = r ? ? ? ? ? ? p p 4 . 24 2 cos . 24 2 ? r = 48 cm 16. 1 4 I I 2 1 = or 2 1 l l = 1 2 ? 2 2 1 2 1 min max 1 I / I 1 I / I I I ? ? ? ? ? ? ? ? - + = = 9 1 2 1 2 2 = ? ? ? ? ? ? - + ?L 1 - L 2 = 10 log 0 min 0 max I I log 10 I I - = 10 log min max I I = 10 log (9) = 20 log (3) 17. Frequency recorded by motorcyclist from police car N” motor = p p m n v c v c × - - . Frequency recorded by motorcyclist from stationary car = c m n v c c × - For no beats c m p p m n v c c n v c v c × - = × - - . Putting the given values, v m = 22 m/s 18. For x = 5, y = 4 sin ? ? ? ? ? ? p 15 5 cos (96 pt) = 2 3 cos (96 pt). So, y will be maximum when cos (96 pt) = max. = 1 Y max. = 2 3 cm at x = 5. 19. At node amplitude of the wave is zero So 4 sin ( px/15) = 0 ? x = 0, 15, 30, 45, 60 20. For the production of beats the two sources must have different frequencies, same amplitude and same phase. It should be remembered that different amplitude affect the maximum and minimum amplitude of beats and different phase affect the time of occurrence of minimum and maximum 21. (b) Note that of y = A sin ?t Then a = - ? 2 A sin ?t That a the y differ in phase by p Which is the case with option B 22. (c) 23. (b) 24. The particle will come after a time T/4 to its mean position. 25. Frequency = 60 60 360 × = 360 Hz. 26. (d) The velocity of sound ? = . P ? ? The presence of moisture in air on a rainy day decreases the density of air since ? ? ? 1 , the velocity of sound increases. 27. (d) The bulk’s modulus for adiabatic process is more than the bulk’s modulus for an isothermal process. I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.doc Page 5 [1] (Waves & Oscillations) 1. A particle of mass m g is executing S.H. M. about a point with amplitude 10- cm. Its maximum velocity is 100 cms –1 . Its velocity will be 50 cms –1 at a distance (a) 5 cm (b) 5 2 cm (c) 3 5 cm (d) 2 10 cm 2. A S.H.M. oscillator has period of 0.1 sec and amplitude of 0.2 m. The maximum velocity is given by (a) 100 ms –1 (b) 4 p ms –1 (c) 100 p ms –1 (d) 20 p ms –1 3. If a hole is drilled along the diameter of the earth and a stone is dropped into it. The stone (a) reaches the centre of earth and stops (b) reaches the opposite end and stops (c) executes S.H.M. about the centre of earth (d) reaches the opposite side and escapes earth 4. Total energy of the particles executing S.H. M is proportional to (a) displacement of the particle (b) frequency of oscillation (c) square of the amplitude (d) velocity at the mean position 5. A pendulum suspended to the celling of a train has a period T when the train is at rest. If the train is accelerated uniformly, the period will (a) Increase (b) decrease (c) remain the same (d) become infinite 6. A pendulum is first vibrated on the surface of earth. Its period is T. It is then taken to the surface of moon where acceleration due to gravity is 1/6 th of that on earth. Its period will be (a) 6 T (b) 3 T (c) 3 T (d) 6 T 7. The angular frequency of a pendulum is ? rad s –1 . If the length is made one fourth of the orginal length, the angular frequency becomes (a) 2 ? (b) 2 ? (c) 4 ? (d) ?/4 8. A simple pendulum has a bob which is given negative charge. It is then allowed to oscillate just above a uniformly positively charged plate, its period (a) remains the same (b) decreases (c) increases (d) no vibration is possible 9. A particle moves such that its motion is represented by a = kx, where ‘a’ is the acceleration and x is displacement and k is a constant. The period of oscillation is (a) 2 p k (b) k 2 p (c) k 2 p (d) none of these 10. A simple pendulum consists of a bob of radius r and mass m and its period is 2 sec. When its bob is replaced by a bob of mass 2m but same radius r, the time period of motion is (a) 4 sec (b) 2 sec (c) 6 sec (d) 8 sec 11. A simple pendulum has a period T inside a lift when it is stationary. The lift is accelerated upwards with constant acceleration ‘a’ . The period (a) decreases (b) increases (c) remains same (d) sometimes increases and sometimes decreases 12. In above question if lift is accelerated downwards with constant acceleration, the period (a) decreases b) increases (c) remains same (d) none 13. The angular velocities of three bodies in simple harmonic motion are ? 1 , ? 2 , ? 3 with their respective amplitude as A 1 , A 2 , A 3 . If all the three bodies have same mass and maximum velocity, then : (a) A 2 1 ? 2 1 = A 2 2 ? 2 2 = A 2 3 ? 2 3 (b) A 2 1 ? 1 = A 2 2 ? 2 = A 2 3 ? 3 (c) A 1 ? 2 1 = A 2 ? 2 2 = A 3 ? 2 3 (d) A 1 ? 1 = A 2 ? 2 = A 3 ? 3 14. In arrangement shown in Fig., if the block of mass ‘m’ is displaced and then released the frequency of oscillation is given by : [2] (a) v = m k k 2 1 2 1 - p (b) v = m k k 2 1 2 1 + p (c) v = 2 1 k k m 2 1 - p (d) v = 2 1 k k m 2 1 + p 15. A pendulum bob has a period 24 s. Its velocity 4 sec after it has passed the mean position is 6.28 cm s - 1 . The amplitude of its motion is : (a) 12 cm (b) 24 cm (c) 48 cm (d) 40 cm 16. The ratio of intensities between two coherent sound sources is 4 : 1. The difference of loudness in decibels (dB) between maximum and minimum intensities when they interfere in space is : (a) 10 log (2) (b) 20 log (3) (c) 10 log (3) (d) 10 log (2) 17. A motorcyclist is moving towards a stationary car which is emitting a sound of 165 Hz, and a police car is chasing the motorcyclist blowing siren at frequency 172 Hz. If speed of police car is 22 m/s, then the speed of motorcyclist for which the motorcyclist hears no beats is : (a) 33 m/s (b) 22 m/s (c) 11 m/s (d) zero 18. The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y = 4 sin ( px/15) cos (96 pt), where x and y are in cm and t in seconds. The maximum displacement at x = 5 cm is : (a) 2 3 cm (b) 3 2 cm (c) 2 cm (d) 3 cm 19. In the above question, the nodes are located along the string at : (a) 0, 15, 30, 45, 60 (b) 0, 20, 40, 60 (c) 0, 10, 20, 30, 40, 50, 60 (d) 0, 20, 40, 80 20. For production of beats the two sources must have : (a) different frequencies and same amplitude (b) different frequencies (c) different frequencies, same amplitude and same phase (d) different frequencies and same phase 21. The displacement versus time graph of SHM is given below : Which of the following is its acceleration versus time graph ? 22. Velocity of sound in a gas is proportional to : (a) square root of isothermal elasticity (b) adiabatic elasticity (c) square root of adiabatic elasticity (d) isothermal elasticity 23. Mechanical wave (sound wave) in a gas is : (a) transverse (b) longitudinal (c) neither transverse nor longitudinal (d) either transverse dependent 24. A particle on the trough of a wave at any instant will come to the mean position after a time (T = time period) : (a) T/2 (b) T/4 (c) T (d) 2T 25. The disc of a siren containing 60 holes rotates at a constant speed of 360 rpm. The emitted sound is in unison with a tuning fork of frequency : (a) 10 Hz (b) 360 Hz (c) 216 Hz (d) 6 Hz In every question a statement of ASSERTION is followed by a statement of REASON. Mark the correct answer out of the following choices: [3] (a) If both ASSERTION and REASON are true and reason is the correct explanation of the assertion. (b) If both ASSERTION and REASON are true but reason is not the correct explanation of the assertion. (c) If ASSERTION is true but REASON is false. (d) If ASSERTION is false but REASON is true. 26. Assertion: Sound travels slower on a rainy day than on a dry day Reason: Moisture decreases the pressure 27. Assertion: The coefficient of adiabatic elasticity is smaller than the coefficient of isothermal elasticity. Reason: Heat is exchanged freely in an adiabatic change but not in an isothermal change. 28. Assertion: The amplitude of an oscillating pendulum decreases gradually with time. Reason: The frequency of the pendulum decreases with time. 29. Assertion: The time period of a simple pendulum inside a lift falling freely is zero. Reason: A body falling freely has infinite acceleration. 30. Assertion: When a spring is cut into 4 equal parts, the force constant becomes 4 times Reason: When two springs of spring constant k 1 and k 2 are connected in parallel, the force constant of combination become k 1 + k 2 . Test- 05 (Waves & Oscillations) ANSWERS 1 C 6 D 11 A 16 B 21 B 26 D 2 B 7 B 12 B 17 B 22 C 27 D 3 C 8 B 13 D 18 A 23 B 28 C 4 C 9 B 14 B 19 A 24 B 29 D 5 B 10 B 15 C 20 C 25 B 30 B SOLUTIONS 1. v max = r ? ? 100 = 10. ? ? ? = 10 rad/s Now v 2 = ? 2 (r 2 - y 2 ) ? 2500 = 100 (100 - y 2 ) y 2 = 100 - 25 = 75 y = 5 3 cm 2. w = T 2 p and v max = r ?, v max = 0.2 × 1 . 0 2 p = 4 p m/s 3. A stone dropped in tunnel along the diameter of earth executes S.H.M. motion as acceleration is proportional to displacement from mean position is directed towards centre of earth. At depth d, g’ ? ? ? ? ? ? - R d 1 , = g ? ? ? ? ? ? - R d R 4. E = 2 1 mr 2 ? 2 ? E ? r 2 5. When train accelerates, then net acceleration is a’ = 2 2 a g + ? a’ > g ? T ? on accelerati 1 ? Time period decreases 6. 2 1 1 2 a a T T = ? T 2 = T 6 T 6 / g g = 7. ? = 2 pv = 2 p × p 2 1 l g = l g ? ?’ = l g 2 l g 4 4 l g = = ? ?’ = 2 ? 8. Due to attractive force of electrostatic field of positive charge, time period will decreases. [4] 9. Time period of S.H.M. is T = 2 p on accelerati nt displaceme ? T = 2 p kx x ? T = k 2 p 10. Time period is independent of mass of bob so long as length remains constant. 11. When the lift ascends with acceleration a then apparent value of acceleration due to gravity becomes (g + a) As T = 2 p g ? . So the time period decreases. 12. During downward motion apparent value of g becomes (g - a). As T ? g 1 ? Time period increases 13. The general equation for a body executing simple harmonic motion is given by : y = A sin ?t. Velocity is given by : ? = dt d dt dy = (A sin ?t) = A ? cos ?t. For maximum velocity, we put cos ?t = 1 Hence, ? max. = A ? Now, since the velocities of three bodies are same, therefore we have : ? 1 = ? 2 = ? 3 A 1 ? 1 = A 2 ? 2 = A 2 ? 3 14. In this case springs are in parallel. ? k p = k 1 + k 2 ? T = 2 p 2 1 k k m + = ? = m k k 2 1 2 1 + p 15. Use v = r ? cos ?t, 6.28 = r ? ? ? ? ? ? p p 4 . 24 2 cos . 24 2 ? r = 48 cm 16. 1 4 I I 2 1 = or 2 1 l l = 1 2 ? 2 2 1 2 1 min max 1 I / I 1 I / I I I ? ? ? ? ? ? ? ? - + = = 9 1 2 1 2 2 = ? ? ? ? ? ? - + ?L 1 - L 2 = 10 log 0 min 0 max I I log 10 I I - = 10 log min max I I = 10 log (9) = 20 log (3) 17. Frequency recorded by motorcyclist from police car N” motor = p p m n v c v c × - - . Frequency recorded by motorcyclist from stationary car = c m n v c c × - For no beats c m p p m n v c c n v c v c × - = × - - . Putting the given values, v m = 22 m/s 18. For x = 5, y = 4 sin ? ? ? ? ? ? p 15 5 cos (96 pt) = 2 3 cos (96 pt). So, y will be maximum when cos (96 pt) = max. = 1 Y max. = 2 3 cm at x = 5. 19. At node amplitude of the wave is zero So 4 sin ( px/15) = 0 ? x = 0, 15, 30, 45, 60 20. For the production of beats the two sources must have different frequencies, same amplitude and same phase. It should be remembered that different amplitude affect the maximum and minimum amplitude of beats and different phase affect the time of occurrence of minimum and maximum 21. (b) Note that of y = A sin ?t Then a = - ? 2 A sin ?t That a the y differ in phase by p Which is the case with option B 22. (c) 23. (b) 24. The particle will come after a time T/4 to its mean position. 25. Frequency = 60 60 360 × = 360 Hz. 26. (d) The velocity of sound ? = . P ? ? The presence of moisture in air on a rainy day decreases the density of air since ? ? ? 1 , the velocity of sound increases. 27. (d) The bulk’s modulus for adiabatic process is more than the bulk’s modulus for an isothermal process. I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.doc [5] K a = ? K i where ? = 1 C C v p > Hence K a > K i Heat is exchanged freely in isothermal process whereas in adiabatic process the heat remain constant. 28. (c) Frequency, in case of simple pendulum, is given by ? = l g 2 1 p . The above expression shows that frequency is independent of amplitude. So, even if frequency remains same, amplitude constantly decreases due to friction of air and other factors. So, assertion and reason are not related to each other. 29. (d) Time period of simple pendulum is given by T = 2 p g l when the lift is falling freely, then g = 0. Therefore T = 8 30. (b) If K be the force constant of each of the part of spring when spring is cut into four parties, the K 1 K 1 K 1 K 1 k 1 + + + = or K 1 = K 4 or K = 4k. Where k is the force constant of the spring initially. I:\anmol\Anajana - Chemistry\Waves & Oscillations MCQ.docRead More

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