Physics for Scientists and Engineers with Modern Physics, Technology Update
Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 16, Problem 15P

(a)

To determine

The transverse speed of the wave.

(a)

Expert Solution
Check Mark

Answer to Problem 15P

The transverse speed of the wave is 1.51m/s_.

Explanation of Solution

Write the general expression for wave function of a wave moving in positive x direction.

  y=Asin(kxωt+ϕ)                                                                                                (I)

Here, A is the amplitude of the wave, k is the wave number, ω is the angular frequency, and ϕ is the phase.

The wave function of the given wave.

  y=(0.120)sin(π8x+4πt)                                                                             (II)

The transverse speed will be obtained by taking the derivative of the position of the wave.

The expression for maximum speed is.

  υy=yt                                                                                                         (III)

Conclusion:

Substitute, (0.120)sin(π8x+4πt)0.100sin(πxπt) for y in equation (III).

  υy=((0.120)sin(π8x+4πt))t=0.120(4π)cos(π8x+4πt)                                                                      (IV)

Substitute, 0.200s for t, and 1.60m for x in equation (IV).

  υy=0.120(4π)cos(π8(1.60m)+4π(0.200s))=1.51m/s

Therefore, the transverse speed of any element on the string is 1.51m/s_.

(b)

To determine

The transverse acceleration at t=0.200s, and x=1.60m.

(b)

Expert Solution
Check Mark

Answer to Problem 15P

The transverse acceleration at t=0.200s, and x=1.60m is 0_.

Explanation of Solution

Transverse acceleration will be obtained by taking the derivative of transverse velocity with respect to time.

Write the expression for transverse acceleration.

  ay=υyt                                                                                                        (V)

Conclusion:

Substitute, 0.120(4π)cos(π8x+4πt) for υy in equation (V).

  ay=(0.120(4π)cos(π8x+4πt))t=0.120(4π)2sin(π8x+4πt)                                                                      (VI)

Substitute, 0.200s for t, and 1.60m for x in equation (VI).

  ay=0.120(4π)2sin(π8(1.60m)+4π(0.200s))=0

Therefore, the transverse acceleration at t=0.200s, and x=1.60m is 0_.

(c)

To determine

The wavelength of the wave.

(c)

Expert Solution
Check Mark

Answer to Problem 15P

The wavelength of the wave is 1.60m_.

Explanation of Solution

Write the expression for wavelength of the wave in terms of wave number.

  λ=2πk                                                                                                       (VII)

Here, k is the wave number.

Comparing equation (I) and (II), the wave number is π8.

Conclusion:

Substitute, π8 for k in equation (V).

  λ=2π(π8)=1.60m

Therefore, the wavelength of the wave is 1.60m_.

(d)

To determine

The period of the wave.

(d)

Expert Solution
Check Mark

Answer to Problem 15P

The period of the wave is 0.500s_.

Explanation of Solution

Write the expression for the period of the wave.

  T=2πω                                                                                                      (VIII)

Here, ω is the angular frequency

Comparing equation (I) and (II), the angular frequency is 4π.

Conclusion:

Substitute, 4π for ω in equation (VI)

  T=2π4π=0.500s

Therefore, the period of the wave is 0.500s_.

(e)

To determine

The speed of an element of propagation of wave.

(e)

Expert Solution
Check Mark

Answer to Problem 15P

The speed of an element of propagation of wave is 32.0m/s_.

Explanation of Solution

Write the expression for speed.

  υ=fλ=λT (IX)

Conclusion:

Substitute, 1.60m for λ , and 0.500s for T in equation (IX).

  υ=1.60m0.500s=32.0m/s

Therefore, the speed of an element of propagation of wave is 32.0m/s_.

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Chapter 16 Solutions

Physics for Scientists and Engineers with Modern Physics, Technology Update

Ch. 16 - Prob. 6OQCh. 16 - Prob. 7OQCh. 16 - Prob. 8OQCh. 16 - Prob. 9OQCh. 16 - Prob. 1CQCh. 16 - Prob. 2CQCh. 16 - Prob. 3CQCh. 16 - Prob. 4CQCh. 16 - Prob. 5CQCh. 16 - Prob. 6CQCh. 16 - Prob. 7CQCh. 16 - Prob. 8CQCh. 16 - Prob. 9CQCh. 16 - A seismographic station receives S and P waves...Ch. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Two points A and B on the surface of the Earth are...Ch. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - When a particular wire is vibrating with a...Ch. 16 - Prob. 11PCh. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - Prob. 15PCh. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - A sinusoidal wave traveling in the negative x...Ch. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - An Ethernet cable is 4.00 m long. The cable has a...Ch. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - Tension is maintained in a string as in Figure...Ch. 16 - Prob. 30PCh. 16 - Prob. 31PCh. 16 - Prob. 32PCh. 16 - Transverse waves are being generated on a rope...Ch. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - A horizontal string can transmit a maximum power...Ch. 16 - Prob. 39PCh. 16 - A two-dimensional water wave spreads in circular...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Show that the wave function y = eb(x vt) is a...Ch. 16 - Prob. 44PCh. 16 - Prob. 45APCh. 16 - Prob. 46APCh. 16 - Prob. 47APCh. 16 - Prob. 48APCh. 16 - Prob. 49APCh. 16 - Prob. 50APCh. 16 - A transverse wave on a string is described by the...Ch. 16 - A sinusoidal wave in a string is described by the...Ch. 16 - Prob. 53APCh. 16 - Prob. 54APCh. 16 - Prob. 55APCh. 16 - Prob. 56APCh. 16 - Prob. 57APCh. 16 - Prob. 58APCh. 16 - A wire of density is tapered so that its...Ch. 16 - Prob. 60APCh. 16 - Prob. 61APCh. 16 - Prob. 62APCh. 16 - Prob. 63APCh. 16 - Prob. 64CPCh. 16 - Prob. 65CPCh. 16 - Prob. 66CPCh. 16 - Prob. 67CP
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