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# ch16 - Chapter 16 WAVES I 1 For a transverse wave on a...

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Chapter 16: WAVES – I 1. For a transverse wave on a string the string displacement is described by y ( x, t ) = f ( x at ), where f is a given function and a is a positive constant. Which of the following does NOT necessarily follow from this statement? A. The shape of the string at time t = 0 is given by f ( x ). B. The shape of the waveform does not change as it moves along the string. C. The waveform moves in the positive x direction. D. The speed of the waveform is a . E. The speed of the waveform is x/t . ans: E 2. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave? ←−−−−−−− A −−−−−−−→ ←−− E −−→ ←−− C −−→ | B | D . . . n v . ans: D 3. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the wavelength of the wave? ←−−−−−−− A −−−−−−−→ ←−− E −−→ ←−− C −−→ | B | D . . . n v . ans: A Chapter 16: WAVES – I 239

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4. In the diagram below, the interval PQ represents: time displacement P Q . A. wavelength / 2 B. wavelength C. 2 × amplitude D. period / 2 E. period ans: D 5. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The correct relationship is: A. f = 1 /T B. f = v + T C. f = vT D. f = v/T E. f = T/v ans: A 6. Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The angular frequency is given by: A. 1 /T B. 2 π /T C. vT D. f/T E. T/f ans: B 7. The displacement of a string is given by y ( x, t ) = y m sin( kx + ω t ) . The wavelength of the wave is: 240 Chapter 16: WAVES – I
8. Three traveling sinusoidal waves are on identical strings, with the same tension. The math- ematical forms of the waves are y 1 ( x, t ) = y m sin(3 x 6 t ), y 2 ( x, t ) = y m sin(4 x 8 t ), and y 3 ( x, t ) = y m sin(6 x 12 t ), where x is in meters and t is in seconds. Match each mathematical form to the appropriate graph below. x y . i x y . ii x y . iii 9. The displacement of a string is given by y ( x, t ) = y m sin( kx + ω t ) . The speed of the wave is: 10. A wave is described by y ( x, t ) = 0 . 1 sin(3 x +10 t ), where x is in meters, y is in centimeters, and t is in seconds. The angular wave number is: A. 0 . 10 rad / m B. 3 π rad / m C. 10) rad / m D. 10 π ) rad / m E. 3 . 0 rad / cm ans: E

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