# Waves - Chapter No 15

Right Answers have been shown below in red color.

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

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.

2. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave? 3. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the wavelength of the wave? 4. In the diagram below, the interval PQ represents: A. wavelength/2
B. wavelength
C. 2 × amplitude
D. period/2
E. period

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

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. 2π/T
C. vT
D. f /T
E. T /f

7. The displacement of a string is given by y(x, t) = ym sin(kx + ωt). The wavelength of the wave is:
A. 2πk/ω B. k/ω C. ωk D. 2π/k E. k/2π

8. Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are y1(x, t) = ym sin(3x − 6t), y2(x, t) = ym sin(4x − 8t), and y3(x, t) = ym sin(6x − 12t), where x is in meters and t is in seconds. Match each mathematical
form to the appropriate graph below. A. y1: i, y2: ii, y3: iii
B. y1: iii, y2: ii, y3: i
C. y1: i, y2: iii, y3: ii
D. y1: ii, y2: i, y3: iii
E. y1: iii, y2: i, y3: ii

9. The displacement of a string is given by y(x, t) = ym sin(kx + ωt). The speed of the wave is:

A. 2πk/ω
B. ω/k
C. ωk
D. 2π/k
E. k/2π

10. A wave is described by y(x, t)=0.1 sin(3x+ 10t), where x is in meters, y is in centimeters, and t is in seconds. The angular wave number is:

11. A wave is described by y(x, t)=0.1 sin(3x−10t), where x is in meters, y is in centimeters, and t is in seconds. The angular frequency is:

12. Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. The speed of these waves is:

A. 0.00021 m/s
B. 2.1 m/s
C. 21 m/s
D. 210 m/s
E. none of these

13. Sinusoidal water waves are generated in a large ripple tank. The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart. The time required for each new whole cycle to be
generated is:

A. 100 s
B. 4.0 s
C. 2.0 s
D. 0.5 s
E. 0.25 s

14. A traveling sinusoidal wave is shown below. At which point is the motion 180◦ out of phase with the motion at point P? 15. The displacement of a string carrying a traveling sinusoidal wave is given by y(x, t) = ym sin(kx − ωt − φ). At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive y direction. The phase constant φ is:

A. 45◦
B. 90◦
C. 135◦
D. 180◦
E. 270◦

16. The displacement of a string carrying a traveling sinusoidal wave is given by y(x, t) = ym sin(kx − ωt − φ). At time t = 0 the point at x = 0 has a velocity of 0 and a positive displacement. The phase constant φ is:

A. 45◦
B. 90◦
C. 135◦
D. 180◦
E. 270◦

17. The displacement of a string carrying a traveling sinusoidal wave is given by y(x, t) = ym sin(kx − ωt − φ). At time t = 0 the point at x = 0 has velocity v0 and displacement y0. The phase constant φ is given by tan φ =:

A. v0/ωy0
B. ωy0/v0
C. 0/y0
D. y0/ωv0
E. ωv0y0

18. A sinusoidal transverse wave is traveling on a string. Any point on the string:

A. moves in the same direction as the wave
B. moves in simple harmonic motion with a different frequency than that of the wave
C. moves in simple harmonic motion with the same angular frequency as the wave
D. moves in uniform circular motion with a different angular speed than the wave
E. moves in uniform circular motion with the same angular speed as the wave

19. Here are the equations for three waves traveling on separate strings. Rank them according to the maximum transverse speed, least to greatest.
wave 1: y(x, t) = (2.0 mm) sin[(4.0 m−1)x − (3.0 s−1)t]
wave 2: y(x, t) = (1.0 mm) sin[(8.0 m−1)x − (4.0 s−1)t]
wave 3: y(x, t) = (1.0 mm) sin[(4.0 m−1 − )x (8.0 s−1)t]

A. 1, 2, 3
B. 1, 3, 2
C. 2, 1, 3
D. 2, 3, 1
E. 3, 1, 2

20. The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is: A. ↑
B. ↓
C. →
D. ←
E. no direction since v = 0