Page 1 Introductory Exercise 15.2 Q 1. Two pulses of identical shape overlap such that the displacement of the rope is momentarily zero at all points, what happens to the energy at this time? Q 2. The pulse shown in figure has a speed of 10 cm/s. (a) If the linear mass density of the right string is 0.25 that of the left string, at what speed does the transmitted pulse travel? (b) Compare the heights of the transmitted pulse and the reflected pulse to that of the incident pulse. Q 3. A wave y i = 0.3 cos (2.0 x - 40t) is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if . (a) the string has a fixed end at x = 0 and (b) the string has a free end at x = 0. Assume SI units. Q 4. The harmonic wave y i = (2.0 × 10 -3 ) cos ?(2.0x - 50t) travels along a string toward a boundary at x = 0 with a second string. The wave speed on the second string is 50 m/s. Write expressions for reflected and transmitted waves. Assume SI units. Q 5. A string that is 10 cm long is fixed at both ends. At t = 0, a pulse travelling from left to right at 1 cm/s is 4.0 cm from the right end as shown in figure. Determine the next two times when the pulse will be at that point again. State in each case whether the pulse is upright or inverted. Q 6. Two pulses travelling in opposite directions along a string are shown for t = 0 in the figure. Plot the shape of the string at t = 1.0, 2.0, 3.0, 4.0 and 5.0 s respectively. Solutions Page 2 Introductory Exercise 15.2 Q 1. Two pulses of identical shape overlap such that the displacement of the rope is momentarily zero at all points, what happens to the energy at this time? Q 2. The pulse shown in figure has a speed of 10 cm/s. (a) If the linear mass density of the right string is 0.25 that of the left string, at what speed does the transmitted pulse travel? (b) Compare the heights of the transmitted pulse and the reflected pulse to that of the incident pulse. Q 3. A wave y i = 0.3 cos (2.0 x - 40t) is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if . (a) the string has a fixed end at x = 0 and (b) the string has a free end at x = 0. Assume SI units. Q 4. The harmonic wave y i = (2.0 × 10 -3 ) cos ?(2.0x - 50t) travels along a string toward a boundary at x = 0 with a second string. The wave speed on the second string is 50 m/s. Write expressions for reflected and transmitted waves. Assume SI units. Q 5. A string that is 10 cm long is fixed at both ends. At t = 0, a pulse travelling from left to right at 1 cm/s is 4.0 cm from the right end as shown in figure. Determine the next two times when the pulse will be at that point again. State in each case whether the pulse is upright or inverted. Q 6. Two pulses travelling in opposite directions along a string are shown for t = 0 in the figure. Plot the shape of the string at t = 1.0, 2.0, 3.0, 4.0 and 5.0 s respectively. Solutions 1. All particles between A and B are at mean positions. So they have maximum kinetic energy. Half of the particles are moving up and other half are moving down. 2. (a) ? of RHS is 1 4th . Hence sloped of transmitted wave on RHS will be two times. (b) v 1 = 10 cm/s and v 2 = 20 cm/s 3. From fixed end there will be a phase change of ?. Further, wave will start travelling in opposite direction. Hence ?t and kx both will now become position. From free end there is no change in phase. 4. il vv k ? ?? v 1 = v 2 = 50 m/s Since, v 2 > v 1 wave is reflected from rarer medium So, there is no phase change in reflected wave. In transmitted wave ? will remain unchanged. v 2 has become two times, hence k 2 will remain half (k = v/ ?) and there is no change in direction of motion of wave and phase. = 2.67 × 10 -4 m Since medium is same, v, ? and k all are same. Only direction of wave motion is changed. Page 3 Introductory Exercise 15.2 Q 1. Two pulses of identical shape overlap such that the displacement of the rope is momentarily zero at all points, what happens to the energy at this time? Q 2. The pulse shown in figure has a speed of 10 cm/s. (a) If the linear mass density of the right string is 0.25 that of the left string, at what speed does the transmitted pulse travel? (b) Compare the heights of the transmitted pulse and the reflected pulse to that of the incident pulse. Q 3. A wave y i = 0.3 cos (2.0 x - 40t) is travelling along a string toward a boundary at x = 0. Write expressions for the reflected waves if . (a) the string has a fixed end at x = 0 and (b) the string has a free end at x = 0. Assume SI units. Q 4. The harmonic wave y i = (2.0 × 10 -3 ) cos ?(2.0x - 50t) travels along a string toward a boundary at x = 0 with a second string. The wave speed on the second string is 50 m/s. Write expressions for reflected and transmitted waves. Assume SI units. Q 5. A string that is 10 cm long is fixed at both ends. At t = 0, a pulse travelling from left to right at 1 cm/s is 4.0 cm from the right end as shown in figure. Determine the next two times when the pulse will be at that point again. State in each case whether the pulse is upright or inverted. Q 6. Two pulses travelling in opposite directions along a string are shown for t = 0 in the figure. Plot the shape of the string at t = 1.0, 2.0, 3.0, 4.0 and 5.0 s respectively. Solutions 1. All particles between A and B are at mean positions. So they have maximum kinetic energy. Half of the particles are moving up and other half are moving down. 2. (a) ? of RHS is 1 4th . Hence sloped of transmitted wave on RHS will be two times. (b) v 1 = 10 cm/s and v 2 = 20 cm/s 3. From fixed end there will be a phase change of ?. Further, wave will start travelling in opposite direction. Hence ?t and kx both will now become position. From free end there is no change in phase. 4. il vv k ? ?? v 1 = v 2 = 50 m/s Since, v 2 > v 1 wave is reflected from rarer medium So, there is no phase change in reflected wave. In transmitted wave ? will remain unchanged. v 2 has become two times, hence k 2 will remain half (k = v/ ?) and there is no change in direction of motion of wave and phase. = 2.67 × 10 -4 m Since medium is same, v, ? and k all are same. Only direction of wave motion is changed. 5. After one reflection from fixed boundary wave is inverted. = 20 s After two times reflection from fixed boundaries wave pulse will again become upright. 6. Let us plot at t = 3 s Net y = y 1 + y 2 Similarly we can draw at other times.Read More

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