1. d and e. The wave speed depends on properties of the medium, not on how you generate the wave. For a string, $v=\sqrt{T_{\text{s}}/\mu }$. Increasing the tension or decreasing the linear density (lighter string) will increase the wave speed.

2. b. The wave is traveling to the right at $2.0\text{ m}/\text{s}$, so each point on the wave passes $x=0\text{m}$, the point of interest, 2.0 s before reaching $x=4.0\text{m}$. The graph has the same shape, but everything happens 2.0 s earlier.

3. d. The wavelength—the distance between two crests—is seen to be 10 m. The frequency is $f=v/\text{λ}=(50\text{m/s})/(10\text{m})=5\text{Hz}$.

4. $n{}_{\text{C}}>n{}_{\text{A}}>n{}_{\text{B}}$. $\text{λ}={\text{λ}}_{\text{vac}}/n$, so a shorter wavelength corresponds to a larger index of refraction.

5. e. A crest and an adjacent trough are separated by $\text{λ}/2$. This is a phase difference of $\pi \text{rad}$.

6. c. Any factor-of-2 change in intensity changes the sound intensity level by 3 dB. One trumpet is ${\displaystyle \frac{1}{4}}$ the original number, so the intensity has decreased by two factors of 2.

7. c. Zack hears a higher frequency as he and the source approach. Amy is moving with the source, so $f_{\text{Amy}}=f_0$.

1. 110 N

3. 2.0 m

5.

7.

9.

11.

1. 4.2 m

2. 48 Hz

13.

1. 20 Hz

2. 23.4 m

3. 45 m/s

15. $v=\sqrt{d/c}$

17. 510 MHz

19.

1. 2.96 m

2. 116 Hz

21.

1. 10 GHz

2. 0.17 ms

23. 2.99 mm

25.

1. $1.5\times {10}^{-11}\text{s}$

2. 3.4 mm

27.

1. 311 m/s

2. 361 m/s

29. 40 cm

31.

1. $-2.0\text{m}$

2. 4.6 m

33. $6.0\times {10}^5\text{J}$

35. 110 dB

37. $2700{\text{W/m}}^2\text{,}1400{\text{W/m}}^2\text{,}610\text{W}\text{/}{\text{m}}^2$

39. 50 m

41.

1. 650 Hz

2. 560 Hz

43. 38.1 m/s

45.

1. 10 m/s

2. ${\displaystyle \frac{5\pi }{6}}\text{rad}$

3. $D(x\text{,}t=0)=A\text{sin}({\displaystyle \frac{2\pi x}{\text{λ}}}+{\varphi }_0)$

47. 2.3 m, 1.7 m

49. 459 nm

51. $410\mu \text{s}$

53. 987 m/s

55.

1. $-x-\text{direction}$

2. 23 m/s, 5.0 Hz, 2.6 rad/m

3. $-1.5\text{cm}$

57. $-19\text{m}\text{/}\text{s}$, 0 m/s, 19 m/s

59. $v=\sqrt{\frac{T_{\text{S}}}{\mu }}=\sqrt{\frac{Mgsin\theta }{\mu }}$

61. $0.07\text{°}\text{C}$

63. 1.8 mm

65. $1.2\times {10}^2\text{ mm\hspace{0.05em}/}\text{s}$

67. $2.0\times {10}^{-5}{\text{W/m}}^2$

69.

1. $250\mu \text{W}\text{/}{\text{m}}^2$

2. 16 km

71.

1. 1.1 kHz

2. 78 dB

73. 41 Hz

75. 620 Hz, 580 Hz

79. Receding at $1.5\times {10}^6\text{m}\text{/}\text{s}$

81. 19 m/s

85. 29 s