PHYS 102 Previous Exam Problems

PHYS 102 Previous Exa Probles CHAPTER 16 Waves Transverse waves on a string Power Interference of waves Standing waves Resonance on a string 1. The displaceent of a string carrying a traveling sinusoidal wave is given by: y ( x, t) = y sin( kx ωt + ϕ). At tie t = 0, the point at x = 0 has a displaceent of zero and is oving in the positive y direction. Find the value of the phase constant φ. (Ans: 180 o ) 2. A stretched string of ass 2.0 g and length 10 c, carries a wave having the following displaceent: y( x, t) = 0.05sin(2π x 400 π t), where x and y are in eters and t is in seconds. What is the tension in the string? (Ans: 800 N) 3. Two identical traveling waves of aplitude 10.0 c, oving in the sae direction, are out of phase by π/4 rad. Find the aplitude of the resultant wave. (Ans: 18.5 c) 4. The equation of a transverse sinusoidal wave traveling along a stretched string is given as follows: y (x,t) = 0.035 sin (0.020x + 4.0t), where x and y are in eters and t is in seconds. What is the transverse speed of the particle at x = 0.035 when t = 0.26 s? (Ans: 7.1 c/s) 5. A standing wave is set up on a string that is fixed at both ends. The standing wave has four loops and a frequency of 600 Hz. The speed of waves on the string is 400 /s. What is the length of the string? (Ans: 1.3 ) 6. A stretched string is 2.70 long, has a ass of 0.260 kg, and is under a tension of 36.0 N. A wave of aplitude 8.50 is traveling on this string. What ust be the frequency of the wave for the average power to be 85.0 W? (Ans: 179 Hz) 7. A stretched string is fixed at both ends. Two adjacent resonant frequencies of the string are 224 Hz and 256 Hz. What is the frequency of the third haronic standing wave pattern? (Ans: 96 Hz) 8. A wave with an aplitude of 1.0 c and wavelength 2.5 is generated on a string with a linear density of 20 g/ that is under a tension of 5.0 N. What is the axiu transverse speed of a point on the string? (Ans: 0.40 /s) 9. A unifor wire, having a ass of 0.4 kg and a length of 6.5, is connected to a pulse generator. The tension is aintained in the wire by suspending a 3.5 kg ass on the other end. Find the tie it takes a pulse to travel fro the pulse generator to the other end. (Ans: 0.28 s) 10. Two identical traveling waves, with a phase difference φ, are oving in the sae direction. If they are interfering and the cobined wave has an aplitude 0.5 ties that of the coon aplitude of the two waves, calculate φ. (Ans: 2.64 rad) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 1

11. A string, fixed at its ends, vibrates according to the equation: y = 0.5 sin(1.5πx) cos(40πt ), where x and y are in eters and t is in seconds. What are the aplitude and velocity of the coponent waves whose superposition can give rise to this wave? (Ans: 0.25, 26.7 /s ) 12. When a wave travels through a ediu, individual particles execute a periodic otion given by the following equation: y = 4.0 sin{π/4(2t+x/8)}, where x and y and are in eters and t is in seconds. What is the phase difference at any given instant between two particles that are 20.0 apart? (Ans: 112.5 ) 13. A string is fixed at both ends. On increasing the tension in the string by 2.5 N, the fundaental frequency is altered in the ratio of 3 : 2. What is the original stretching force? (Ans: 2N) 14. Consider the superposition of the following two sinusoidal waves: y 1 = (4.0 ) sin (2πx 4πt) and y 2 = (4.0 ) sin (2πx+4πt), where x is in eter and t is in second. What will be the distance between any two successive nodes? (Ans: 0.50 ) 15. A particle of a string oves up and down as a traveling sinusoidal wave passes through it. If the tie for that particle to ove fro axiu displaceent to zero displaceent is 0.2 s, what is the frequency of the wave? (Ans: 1.25 Hz) 16. A string is vibrating in its fifth-haronic standing wave pattern described by the equation: y(x,t)= 0.25 sin(πx) cos(15t). Find the length of the string. (Ans: 5 ) 17. A string, under a tension of 100 N, is observed to oscillate at two adjacent resonant frequencies of 300 Hz and 400 Hz. The tension in the string is changed and the string is observed to oscillate at resonant frequencies of 400 Hz and 480 Hz with no interediate frequencies. Find the new tension in the string. (Ans: 64 N) 18. The tension in a string with a linear ass density of 1.0 10-3 kg/ is 0.40 N. What frequency will a sinusoidal wave with a wavelength of 20 c on this string have? (Ans: 100 Hz) 19. A wave is described by y (x, t) = 0.1 sin(3x ωt), where x and y are in eters. If the axiu transverse speed is 60 /s, what is the speed of the wave? (Ans: 200 /s) 20. Two sinusoidal waves having wavelength of 5 and aplitude of 10 c, are traveling in opposite directions on a 20- long stretched string fixed at both ends. Excluding the nodes at the ends of the string, how any nodes appear in the resulting standing wave? (Ans: 7) 21. Two stretched strings have the sae linear density. The tension in the second string is half the tension in the first (τ 2 = τ 1 /2), and its length is only one third the first (L 2 =L 1 /3). Copare the fundaental frequencies for both strings (f 1 /f 2 ). (Ans: 0.47) 22. A transverse sinusoidal wave is traveling on a string with a speed of 300 /s. If the wave has a frequency of 100 Hz, what is the phase difference between two particles on the string that are 85 c apart? (Ans: 1.8 rad) 23. A 50-c long string with a ass of 0.01 kg is stretched with a tension of 18 N between two fixed supports. What is the resonant frequency of the longest wavelength on this string? (Ans: 30 Hz) 24. A transverse sinusoidal wave of frequency 100 Hz is traveling along a stretched string with a speed of 20.0 /s. What is the shortest distance between a crest and a point of zero transverse acceleration? (Ans: 0.05 ) 25. Two waves, each with a speed of 20 /s, interfere on a string fixed at both ends to yield a standing wave given by the equation: y (x,t) = 0.05 sin(k x) cos(30 t), where x and y are in eters and t is in seconds. What is the distance between two consecutive nodes? (Ans: 2.1 ) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 2

26. A 40-c string of linear density 8.0 g/ is fixed at both ends and is driven by a variable frequency oscillator ranged fro 300 Hz to 800 Hz. The string is set in oscillation only at the frequencies of 440 and 600 Hz. Find the tension in the string. (Ans: 131 N) 27. A sinusoidal wave, given by the equation: y (x,t) = 0.07 cos(6.0 x 30 t ), where x and y are in eters and t is in seconds, is oving in a string of linear density =1.2 g/. At what average rate is the energy transferred by the wave? (Ans: 1.32 10-2 W) 28. Two identical sinusoidal waves, that are out of phase with each other, travel in the sae direction. They interfere and produce a resultant wave given by the equation: y (x,t) = 8.0 10-4 sin(4.0 x - 8.0 t + 1.57), where x and y are in eters and t is in seconds. What is the aplitude of the two interfering waves? (Ans: 0.5 ) 29. A string under a tension of 15 N, is set into vibration to produce a wave of speed 20 /s, and a axiu transverse speed of 8.0 /s. For this wave, what is the average power? (Ans: 24 W) 30. A traveling wave is given by: y (x,t) = 6.0 cos(0.63x + 25.1t), where x and y are in c and t is in seconds. It interferes with a siilar wave propagating in the opposite direction to produce a standing wave. What is the distance between a node and the consecutive antinode? (Ans: 2.5 c) 31. A 100-Hz oscillator is used to generate a sinusoidal wave, on a string, of wavelength 10 c. When the tension in the string is doubled, what frequency and wavelength does the oscillator produce? (Ans: 100 Hz and 14 c) 32. The lowest resonant frequency, in a certain string claped at both ends, is 50 Hz. When the string is claped at its idpoint, what is the lowest resonant frequency? (Ans: 100 Hz) 33. A standing wave is established in a 3.0--long string fixed at both ends. The string vibrates in three segents with an aplitude of 1.0 c. If the wave speed is l00 /s, what is the frequency? (Ans: 50 Hz) 34. The axiu aplitude of a standing wave on a string, with linear density = 3.00 g/ and tension of 15.0 N, is 0.20 c. If the distance between adjacent nodes is 12.0 c, what will be the wave function y (x,t) of the standing wave? (Note that x is in centieters and t is in seconds.) Ans: y (x,t) = 0.20 sin(0.262x) cos(1.85 10 3 t) 35. A transverse sinusoidal wave traveling in the negative x direction has an aplitude of 10.0 c, a wavelength of 20.0 c, and a frequency of 8.00 Hz. Write the expression for y as a function of x (in eters) and t (in seconds) if y (0,0) = 10.0 c. Ans : y = (0.1 ) sin[31.4x+50.3t +(π /2)] 36. A haronic wave is described by: y = 0.2 sin(25x 10t) (SI units). How far does a wave crest ove in 20 s? (Ans: 8 ) 37. A stretched string that is fixed at both ends oscillates in a third-haronic standing wave pattern. The distance between two adjacent nodes is 0.75. The tension is varied until the fourth-haronic standing wave is generated on the sae string. What is the distance between two adjacent nodes in this case? (Ans: 0.56 ) 38. Energy is transitted at the rate of P o by a wave of frequency f o on a string under tension τ o. What is the new energy transission rate P in ters of P o if the tension is increased to 4τ o and frequency is decreased to f o /2? (Ans: P o /2) 39. Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance fro the second node to the fifth node is 60 c. What is the wavelength of each of the two original waves? (Ans: 40 c) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 3

40. Two identical strings (sae ass and length), each fixed at both ends, are arranged near each other. If string A starts oscillating in its fundaental ode, it is observed that string B will begin vibrating in its third noral ode (n = 3). What is the ratio of the tension in string B to that in string A? (Ans: 1/9) 41. What phase difference (in ters of the wavelength λ) between two identical traveling waves, oving in the sae direction along a stretched string, results in the cobined wave having an aplitude 1.75 ties that of the coon aplitude of the two cobined waves? (Ans: 0.16 λ) 42. In figure 3, two equivalent pulses, Pulse 1 and Pulse 2, are sent fro points A and B at the sae tie. Which pulse reaches point C first? (Ans: Pulse 1) 43. The displaceent (y) of a vibrating string versus position (x) along the string is shown in figure 4. The wave has a speed of 0.10 /s. What is the axiu transverse speed of a particle on the string? (Ans: 4.2 c/s) 44. Standing waves are produced on a string at the two consecutive resonant frequencies 120 and 160 Hz. If the string has a length of 3.0, what is the distance between two adjacent nodes at the resonant frequency 240 Hz? (Ans: 0.50 ) 45. A steel wire of ass 0.400 kg and length 0.640 supports a 102-kg block (see figure 9). The wire is struck exactly at the idpoint generating a pulse on the wire. How long does it take the peak of the pulse to reach the top of the wire? (Ans: 8.00 s) 46. Vibrations with frequency 600 Hz are set up on a 1.33- length of a string that is claped at both ends. The speed of waves on the string is 400 /s. How far fro either end of the string does the first node occur? (Ans: 0.33 ) 47. Two identical sinusoidal waves are traveling along a stretched string, both oving in the negative x direction. The two waves are out of phase by π radians. The aplitude of each wave is 1.00 c and their frequency is 100 Hz. What is the displaceent of the string at x = 0 when t = 10.0 s? (Ans: zero) 48. Standing waves can be excited on a string of length L = 1.00 whose ends are fixed at x = 0 and x = L. Find the two sallest values of the wave nuber. (Ans: 3.14-1, 6.28-1 ) 49. A wire is held under tension by suspending weights fro an end that passes over a pulley. The speed of transverse waves on the wire is 51 /s. The wire is replaced by another wire with three ties the linear ass density and twice as uch weight is suspended fro the end of the new wire. What is the speed of the traveling waves now? (Ans: 42 /s) 50. A sinusoidal wave is traveling along a stretched string. The oscillator that generates the wave copletes 40 vibrations in 30.0 s. A given peak of the wave travels 4.25 along the string in 10.0 s. What is the wavelength of the wave? (Ans: 0.319 ) 51. Two sinusoidal waves have the sae frequency, the sae aplitude y, and travel in the sae direction in the sae ediu. If the aplitude of the resultant wave is 1.8 y, what is the phase difference between the two waves? (Ans: 0.14 wavelengths) 52. Vibrations with frequency 600 Hz are established on a string of length 1.33 that is claped at both ends. The speed of waves on the string is 400 /s. How any antinodes are contained in the resulting standing wave pattern? (Ans: 4) 53. A stone is dropped into a lake; and it produces circular surface waves with a frequency of 0.25 Hz. When should a second stone be dropped, after the first, at the sae place to produce destructive interference? Ignore the tie it takes the stone to reach water. (Ans: 2.0 s) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 4

54. A transverse sinusoidal wave, travelling in the positive x direction along a string, has an aplitude of 20 c. The transverse position of an eleent of the string at t = 0, x = 0 is y = + 3.0 c, and the eleent has negative velocity. What is the phase constant of this wave? (Ans: 0.15 rad) 55. A standing wave, having three nodes, is set up on a string fixed at both ends. If the frequency of the wave is doubled, how any antinodes will there be? (Ans: 4) 56. A transverse sinusoidal wave travelling on a string is given by: y (x,t) = 0.150 sin (15.7 x 50.3 t) (SI units). At a certain instant, point A is at the origin, and point B is the closest point to A along the x axis where the otion is 60.0 o out of phase with that at A. What is the distance between points A and B? (Ans: 0.0667 ) 57. Two pulses having the sae aplitude and the sae speed v = 1.0 c/s approach each other, as shown in figure 12, which shows their positions at tie t = 0. At what tie will they copletely cancel each other? (Ans: 5.0 s) 58. A string with a length of 2.50 has two adjacent resonances at frequencies 112 Hz and 140 Hz. Deterine the wavelength of the 112 Hz resonance. (Ans: 1.25 ) 59. A standing wave on a string is described by: y (x,t) = 0.040 (sin 5π x) (cos 40 π t) (SI units). If the length of the string is 1.0, what is the haronic nuber of the wave? (Ans: 5) 60. A transverse traveling wave is described by y = 0.15 sin [(π/16) (2x 64t)], where x and y are in eter and t is in second. Deterine the first positive x-coordinate where y is axiu and when t = 0. (Ans: 4.0 ) 61. An 8.00 long wire with a ass of 10.0 g is under a tension of 25.0 N. A transverse wave for which the wavelength is 0.100, and the aplitude is 3.70 is propagating on the wire. What is the agnitude of the axiu transverse acceleration of a point on the wire? (Ans: 2.92 10 5 /s 2 ) 62. A sinusoidal transverse wave travels with a speed of 30 /s on a string of length 8.0 and ass 6.0 g. The average power of the wave is 50.0 W. What is the average power of the wave if the tension is increased such that the wave speed is doubled while keeping both the wavelength and the aplitude fixed? (Ans: 400 W) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 5

A B C D E Conceptual Probles 1. Equations 1-5 describe five sinusoidal waves traveling on five different strings. 1. y(x, t) = 2 sin(2x - 4t) 2. y(x, t) = 2 sin(4x -10t) 3. y(x, t) = 2 sin(6x -12t) 4. y(x, t) = 2 sin(8x -16t) 5. y(x, t) = 2 sin(10x -20t). All strings have the sae tension and all have the sae linear ass density, except one. Which string has the different linear ass density? A. 2 B. 1 C. 5 D. 4 E. 3 2. A traveling sinusoidal wave is shown in the figure 1. At which point is the otion 180 o out of phase with the otion at point P? A. C B. A C. B D. E E. D 3. A sinusoidal transverse wave is traveling on a string. Any point on the string: A. oves in siple haronic otion with the sae angular frequency as the wave. B. oves in the sae direction as the wave. C. oves in siple haronic otion with a different frequency than that of the wave. D. oves in unifor circular otion with a different angular speed than the wave. E. oves in unifor circular otion with the sae angular speed as the wave. 4. Figure 2 shows the displaceents at the sae instant for two waves, P and Q, of equal frequency and having aplitude Y and 2Y, respectively. If the two waves ove along the positive x direction, what is the aplitude of the resultant wave, and the phase difference between the resultant wave and the wave P? A. Resultant aplitude is Y, and the phase difference is π. B. Resultant aplitude is 2Y, and the phase difference is π. C. Resultant aplitude is 3Y, and the phase difference is π. D. Resultant aplitude is Y, and the phase difference is zero. E. Resultant aplitude is 2Y, and the phase difference is zero. 5. Transverse waves, with fixed aplitude, are being generated on a rope under constant tension. When the frequency of the wave is increased, which one of the following stateents is correct? A. The wavelength decreases and the transitted power increases. B. The wavelength increases and the transitted power is the sae. C. The axiu transverse speed is the sae and the transitted power increases. D. Both the wavelength and the linear ass density decrease. E. Both the wavelength and the axiu transverse speed increase. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 6

6. The velocity of a traveling wave on a string under fixed tension: A. does not change when the frequency increases. B. increases when the frequency increases. C. decreases when the frequency increases. D. decreases when the wave length increases. E. decreases when the aplitude increases. 7. Which of the following cannot be a traveling wave? A. cos (kx) sin (ωt) B. sin (kx + ωt) C. cos (kx + ωt) D. cos (φ/2) sin (kx + ωt + φ/2) E. sin k(x-vt) 8. If you set up the fifth haronic on a string that is fixed at both ends, which of the following stateents is correct? A. There is an antinode at the iddle of the string. B. There is a node at the iddle of the string. C. There are five nodes. D. There are four nodes. E. There are four antinodes. 9. Consider the situation shown in figure 5, which of the following stateents is correct? A. Particle 1 is oving upward. B. Particle 3 has zero acceleration. C. Particle 5 has zero velocity. D. Particle 2 is oving downward. E. Particle 4 is oving upward. 10. Figure 6 shows three waves that are separately sent along a string that is stretched under a certain tension. Which of the following stateent is correct? A. Wave 3 has lower frequency than waves 1 and 2. B. Wave 3 has higher speed than waves 1 and 2. C. Wave 3 has lower speed than waves 1 and 2. D. Wave 3 has higher frequency than waves 1 and 2. E. Wave 1 has higher speed than waves 2 and 3. 11. A string is put under tension and then two different sinusoidal waves A and B are separately sent along it. Figure 7 gives plots of the displaceent versus tie for a point on the string. Which of the following stateents is correct? A. Wave A has the sae speed as wave B. B. Wave A has the sae frequency as wave B. C. Wave A has a lower frequency than wave B. D. Wave A has a larger wavelength than wave B. E. Wave A has the sae wave length as wave B. 12. Figure 8 shows a snap shot of part of a transverse wave traveling along a string. Which stateent about the otion of eleents of the string is correct? A. S, the agnitude of its acceleration is a axiu. B. S, the agnitude of its acceleration is zero. C. P, its speed is a axiu. D. Q, its speed is zero. E. Q, its displaceent is a axiu. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 7

13. A wave described by the equation: y (x,t) = A cos (kx ωt). At t = 0, the displaceent is zero at x = A. 1/4 wavelength, 3/4 wavelength,... B. 1/2 wavelength, 1 wavelength,.... C. 1/3 wavelength, 5/3 wavelength,... D. 1/2 wavelength, 3/2 wavelength,... E. 1/5 wavelength, 2/5 wavelength,... 14. A wave on a string is reflected fro a fixed end. The reflected wave: A. is 180 o out of phase with the original wave at the fixed end. B. has a larger speed than the original wave. C. has a larger aplitude than the original wave. D. cannot be transverse. E. is in phase with the original wave at the fixed end. 15. Transverse waves, with fixed aplitude, are being generated on a rope under constant tension. When the frequency of the wave is increased, which one of the following stateents is correct? A. The wavelength decreases and the transitted power increases. B. The wavelength increases and the transitted power is the sae. C. The axiu transverse speed is the sae and the transitted power increases. D. Both the wavelength and the linear ass density decrease. E. Both the wavelength and the axiu transverse speed increase. 16. For a standing wave on a string fixed at both ends A. the idpoint is an antinode for odd haronics. B. the idpoint is an antinode for even haronics. C. the idpoint is a node for odd haronics. D. the shortest wavelength corresponds to the fundaental ode. E. the aplitude of all points on the string is the sae. 17. Two sinusoidal waves having the sae aplitude (A), frequency and wavelength, travel in the sae direction and have a phase difference φ. Which one of the following stateents is true? A. Their interference will be constructive if φ = 100 π. B. Their interference will be constructive if φ = π. C. The resultant wave will be a standing wave for φ = 0. D. For certain values of φ, the aplitude of the resultant reaches 4A. E. The frequency of the resultant wave is twice the original frequency. 18. Which of the following stateents is correct? A. Electroagnetic waves can travel in vacuu. B. Sound waves can travel in vacuu. C. The speed of sound is the sae in all edia. D. The power transitted by a sinusoidal wave on a string decreases with increasing frequency of the wave. E. The power intercepted by a sound detector does not depend on the area of the detector. 19. Under a tension τ, it takes 2 s for a pulse to travel the length of a stretched string. What tension is required for the pulse to take 6 s? A. τ/9 B. τ/2 C. τ/3 D. 3τ E. 4τ Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 8

20. Any point on a string carrying a sinusoidal traveling wave is oving with its axiu transverse speed when: A. the agnitude of its displaceent is zero. B. the agnitude of its acceleration is a axiu. C. the agnitude of its displaceent is a axiu. D. the agnitude of its displaceent is half the aplitude. E. the agnitude of its displaceent is one fourth the aplitude. 21. A stretched string has a ass per unit length of 0.500 kg/ and is under a tension of 10.0 N. A sinusoidal wave on this string has an aplitude of 0.120, a frequency of 100 Hz, and is traveling in the negative x direction. What is the equation of the wave? A. y = (0.120 ) sin(140x + 628t) B. y = (0.120 ) sin(140x - 628t) C. y = (0.120 ) sin(444x + 628t) D. y = (0.120 ) sin(444x - 628t) E. y = (0.060 ) sin(140x + 628t) 22. A sinusoidal traveling wave is generated on a string. The speed of the wave is 0.050 /s, and it is traveling to the right along the x-axis. Figure 10 shows the displaceent of the particle of the string at x = 0 as a function of tie. Find the equation of the wave [y is given in eters]. A. y(x,t) = 0.01 sin[2π(50x 2.5t)] B. y(x,t) = 0.01 sin[2π(50x + 2.5t)] C. y(x,t) = 0.01 sin[2π(50x 5.5t)] D. y(x,t) = 0.01 sin[2π(50x + 5.5t)] E. y(x,t) = 0.02 sin[2π(50x 2.5t)] 23. A unifor chain of length 1.00, having a linear ass density 1.00 kg/, is hanging vertically fro a support, as shown in figure 11. A pulse is sent along it fro the botto. The speed of the pulse at points A, B, and C are v A, v B and v C and respectively: A. v > v > v A B C B. v > v > v C B A C. v > v < v B A C D. v = v = v A B C E. v = v < v A B C 24. The axiu transverse speed for a particle on a string carrying a sinusoidal wave is vs displaceent of a point on the string is half its axiu, what is the speed of the point?. When the A. 3 v s /2 B. vs/2 C. vs/4 D. vs/3 E. 3vs/4 25. Two waves with the sae aplitude y and wavelength λ are oving on a string. One of the waves is shifted relative to the other by a distance of 5.5 λ. The aplitude of the resultant wave is: A. 0 B. 2 y C. 0.50 y D. 2 y cos 30 E. 2 y cos 15 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 9

26. A sinusoidal wave of aplitude y and wavelength λ travels on a stretched string. The ratio of the axiu transverse speed of a particle on the string to the wave speed is: A. 2πy /λ B. 2πλ/y C. 2πy λ D. y /2πλ E. λ/2πy 27. The average power of a sinusoidal wave on a stretched string is P. If an identical wave is sent siultaneously along the sae string in the sae direction but with a phase difference of 90 wave, the new average power is A. 2P B. P C. 4P D. P/4 E. P/2 28. Which one of the following stateents is TRUE concerning the points on a string that sustain a standing wave pattern? A. The aplitude of oscillation is not the sae for all points. B. All points vibrate vertically with the sae speed. C. All points undergo the sae displaceents. D. All points vibrate with different frequencies. E. Soe points undergo otion that is purely longitudinal. 29. A string of length L, ass per unit length µ, and tension τ, is vibrating at its fundaental frequency. If the length of the string is doubled, with all other factors held constant, what is the effect on the fundaental frequency? A. It becoes one half as large. B. It becoes two ties larger. C. It becoes ties as large. D. It becoes 1/ ties as large. E. It does not change. 30. A resultant traveling wave can be produced by an interference between two sinusoidal waves of the sae frequency and aplitude. This interference is fully destructive only if the two waves: A. travel in the sae direction and are 180 out of phase B. travel in opposite directions and are 180 out of phase C. travel in the sae direction and are in phase D. travel in opposite directions and are in phase E. travel in the sae direction and are 90 out of phase o fro the first Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 10

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 16 Page 11