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Page 1 Introductory Exercise 16.1 Q1: Calculate the bulk modulus of air from the following data for a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (10 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10 m. Sol: Q2: Find the minimum and maximum wavelengths of sound in water that is in the audible range for an average human ear. Speed of sound in water is 1450 m/s. Sol: (a) For minimum wavelength n = 20 KHz Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some point x . What is the displacement at that point at t = 0? 5 6 1 Page 2 Introductory Exercise 16.1 Q1: Calculate the bulk modulus of air from the following data for a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (10 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10 m. Sol: Q2: Find the minimum and maximum wavelengths of sound in water that is in the audible range for an average human ear. Speed of sound in water is 1450 m/s. Sol: (a) For minimum wavelength n = 20 KHz Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some point x . What is the displacement at that point at t = 0? 5 6 1 (b) What is the maximum value of the displacement at any time and place ? Take the density of air to be 1.29 kg/m and speed of sound in air is 340 m/s. Sol: (a) Displacement is zero when pressure is maximum. Q4: The pressure variation in a sound wave in air is given by ?P = 12 sin(8.18x  2700t +p/4) N/m Find the displacement amplitude. Density of air = 1.29 kg/m . Sol: In the above problem, we have found that Now substituting the value, we have Introductory Exercise 16.2 Q1: Calculate the temperature at which the velocity of sound in air is double its velocity at 0°C. Sol: Speed of velocity in air is, v ? vT 3 2 3 Page 3 Introductory Exercise 16.1 Q1: Calculate the bulk modulus of air from the following data for a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (10 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10 m. Sol: Q2: Find the minimum and maximum wavelengths of sound in water that is in the audible range for an average human ear. Speed of sound in water is 1450 m/s. Sol: (a) For minimum wavelength n = 20 KHz Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some point x . What is the displacement at that point at t = 0? 5 6 1 (b) What is the maximum value of the displacement at any time and place ? Take the density of air to be 1.29 kg/m and speed of sound in air is 340 m/s. Sol: (a) Displacement is zero when pressure is maximum. Q4: The pressure variation in a sound wave in air is given by ?P = 12 sin(8.18x  2700t +p/4) N/m Find the displacement amplitude. Density of air = 1.29 kg/m . Sol: In the above problem, we have found that Now substituting the value, we have Introductory Exercise 16.2 Q1: Calculate the temperature at which the velocity of sound in air is double its velocity at 0°C. Sol: Speed of velocity in air is, v ? vT 3 2 3 Q2: Calculate the difference in the speeds of sound in air at 3°C, 60 cm pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of sound in air at 0°C is 332 m/s. Sol: v ? vT ? = 330.17 m/s = 349.77 m/s The difference in these two speeds is approximately 20 m/s. Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency 250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of the liquid. Sol: ? B = ? (f?) = (900) (250 × 8) = 3.6 × 10 N/m Q4: Calculate the speed of sound in oxygen at 273 K. Sol: = 315 m/s Introductory Exercise 16.3 Q1: A sound wave in air has a frequency of 300 Hz and a displacement amplitude of 6.0 × 10 3 mm. For this sound wave calculate the (a) pressure amplitude (b) intensity (c) sound intensity level (in dB) 3 2 2 9 2 Page 4 Introductory Exercise 16.1 Q1: Calculate the bulk modulus of air from the following data for a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (10 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10 m. Sol: Q2: Find the minimum and maximum wavelengths of sound in water that is in the audible range for an average human ear. Speed of sound in water is 1450 m/s. Sol: (a) For minimum wavelength n = 20 KHz Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some point x . What is the displacement at that point at t = 0? 5 6 1 (b) What is the maximum value of the displacement at any time and place ? Take the density of air to be 1.29 kg/m and speed of sound in air is 340 m/s. Sol: (a) Displacement is zero when pressure is maximum. Q4: The pressure variation in a sound wave in air is given by ?P = 12 sin(8.18x  2700t +p/4) N/m Find the displacement amplitude. Density of air = 1.29 kg/m . Sol: In the above problem, we have found that Now substituting the value, we have Introductory Exercise 16.2 Q1: Calculate the temperature at which the velocity of sound in air is double its velocity at 0°C. Sol: Speed of velocity in air is, v ? vT 3 2 3 Q2: Calculate the difference in the speeds of sound in air at 3°C, 60 cm pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of sound in air at 0°C is 332 m/s. Sol: v ? vT ? = 330.17 m/s = 349.77 m/s The difference in these two speeds is approximately 20 m/s. Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency 250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of the liquid. Sol: ? B = ? (f?) = (900) (250 × 8) = 3.6 × 10 N/m Q4: Calculate the speed of sound in oxygen at 273 K. Sol: = 315 m/s Introductory Exercise 16.3 Q1: A sound wave in air has a frequency of 300 Hz and a displacement amplitude of 6.0 × 10 3 mm. For this sound wave calculate the (a) pressure amplitude (b) intensity (c) sound intensity level (in dB) 3 2 2 9 2 Speed of sound = 344 m/s and density of air = 1.2 kg/m . Sol: (a) = 4.67 Pa (b) (c) Q2: Most people interpret a 9.0 dB increase in sound intensity level as a doubling in loudness. By what factor must the sound intensity be increased to double the loudness?Sol: Given L  L =9 dB Solving the equation we get, Q3: A baby's mouth is 30 cm from her father's ear and 3.0 m from her mother's ear. What is the, difference between the sound intensity levels heard by the father and by the mother. Sol: ? 3 2 1 Page 5 Introductory Exercise 16.1 Q1: Calculate the bulk modulus of air from the following data for a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (10 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10 m. Sol: Q2: Find the minimum and maximum wavelengths of sound in water that is in the audible range for an average human ear. Speed of sound in water is 1450 m/s. Sol: (a) For minimum wavelength n = 20 KHz Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some point x . What is the displacement at that point at t = 0? 5 6 1 (b) What is the maximum value of the displacement at any time and place ? Take the density of air to be 1.29 kg/m and speed of sound in air is 340 m/s. Sol: (a) Displacement is zero when pressure is maximum. Q4: The pressure variation in a sound wave in air is given by ?P = 12 sin(8.18x  2700t +p/4) N/m Find the displacement amplitude. Density of air = 1.29 kg/m . Sol: In the above problem, we have found that Now substituting the value, we have Introductory Exercise 16.2 Q1: Calculate the temperature at which the velocity of sound in air is double its velocity at 0°C. Sol: Speed of velocity in air is, v ? vT 3 2 3 Q2: Calculate the difference in the speeds of sound in air at 3°C, 60 cm pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of sound in air at 0°C is 332 m/s. Sol: v ? vT ? = 330.17 m/s = 349.77 m/s The difference in these two speeds is approximately 20 m/s. Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency 250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of the liquid. Sol: ? B = ? (f?) = (900) (250 × 8) = 3.6 × 10 N/m Q4: Calculate the speed of sound in oxygen at 273 K. Sol: = 315 m/s Introductory Exercise 16.3 Q1: A sound wave in air has a frequency of 300 Hz and a displacement amplitude of 6.0 × 10 3 mm. For this sound wave calculate the (a) pressure amplitude (b) intensity (c) sound intensity level (in dB) 3 2 2 9 2 Speed of sound = 344 m/s and density of air = 1.2 kg/m . Sol: (a) = 4.67 Pa (b) (c) Q2: Most people interpret a 9.0 dB increase in sound intensity level as a doubling in loudness. By what factor must the sound intensity be increased to double the loudness?Sol: Given L  L =9 dB Solving the equation we get, Q3: A baby's mouth is 30 cm from her father's ear and 3.0 m from her mother's ear. What is the, difference between the sound intensity levels heard by the father and by the mother. Sol: ? 3 2 1 Now Substituting We get, L  L  20 dB Q4: The faintest sound that can be heard has a pressure amplitude of about 2 × 10 N/m and the loudest that can be heard without pain has a pressure amplitude of about 28 N/m . Determine in each case (a) the intensity of the sound both in W/m and in dB and (b) the amplitude of the oscillations if the frequency is 500 Hz. Assume an air density of 1.29 kg/m and a velocity of sound is 345 m/s. Sol: For finest sound, =  3.48 dB Same formulae can be applied for loudest sound. ? For finest sound, = 1.43 × 10 m x1 2 5 2 2 2 3 11Read More
1. What are sound waves? 
2. How does sound travel through different mediums? 
3. What determines the pitch and frequency of sound waves? 
4. How does the amplitude of sound waves affect the volume? 
5. How does the speed of sound change with temperature? 

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