Physics for Scientists and Engineers With Modern Physics
Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 17, Problem 66AP

(a)

To determine

The sound which arrives first.

(a)

Expert Solution
Check Mark

Answer to Problem 66AP

The sound through the metal arrives first.

Explanation of Solution

When a hammer is used at one end, the sound can travel through both metal rod and air. The speed of the wave through metal rod is 3560m/s, and that of speed of the sound in air is 343m/s.

Since, speed of the sound in metal is greater than the sped of the sound in air, the sound through metal arrives first.

Conclusion:

Therefore, the sound through the metal arrives first.

(b)

To determine

The length of the rod as a function of Δt.

(b)

Expert Solution
Check Mark

Answer to Problem 66AP

The length of the rod as a function of Δt is 380Δt_.

Explanation of Solution

Write the expression for the time taken by the sound to travel.

  t=Lυ                                                                                                                         (I)

Here, L is the length of the rod, υ is the speed, and t is the time taken.

The delay between the arrival of pulses through copper and air is.

  Δt=L(1υair1υcu)=Lυcuυairυairυcu                                                                                                   (II)

Here, υair is the speed of the sound in air, υcu is the speed of the sound in copper rod.

Rearrange equation (II) to obtain an expression for L.

  L=υairυcuυcuυairΔt                                                                                                      (III)

Conclusion:

Substitute, 343m/s for υair, and 3560m/s for υcu in equation (III).

  L=(343m/s)(3560m/s)(3560m/s343m/s)Δt=380Δt

Therefore, length of the rod as a function of Δt is 380Δt_.

(c)

To determine

The length of the rod if Δt=127ms.

(c)

Expert Solution
Check Mark

Answer to Problem 66AP

The length of the rod if Δt=127ms is 48.2m_.

Explanation of Solution

Write the expression for the length of the rod.

  L=380Δt                                                                                                              (IV)

Conclusion:

Substitute, 127ms for Δt in equation (IV).

  L=(380m/s)(127ms×103s1ms)=48.2m

Therefore, the length of the rod if Δt=127ms is 48.2m_.

(d)

To determine

The length of the rod in terms of t and υr.

(d)

Expert Solution
Check Mark

Answer to Problem 66AP

The length of the rod in terms of t and υr is L=Δt1343m/s1υr_.

Explanation of Solution

The speed of the sound in rod is given as υr. The speed of the sound in air is 343m/s.

Substitute, υr for υcu, 343m/s for υair in equation (II) and rewrite to obtain an expression for L.

  Δt=L(1343m/s1υr)L=Δt(1343m/s1υr)

Conclusion:

Therefore, the length of the rod in terms of t and υr is L=Δt1343m/s1υr_.

(d)

To determine

The length of the rod when speed of the sound goes to infinity.

(d)

Expert Solution
Check Mark

Answer to Problem 66AP

The length of the rod when speed of the sound goes to infinity is Δt(343m/s)_.

Explanation of Solution

Write the expression for the length of the rod.

  L=Δt(1343m/s1υr)                                                                                                 (V)

Conclusion:

Substitute, for υr in equation (V).

  L=Δt(1343m/s1)=Δt(1343m/s)=Δt(343m/s)

Therefore, the length of the rod when speed of the sound goes to infinity is Δt(343m/s)_.

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Chapter 17 Solutions

Physics for Scientists and Engineers With Modern Physics

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