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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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Section
BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A tunnel under a river is 2.00 km long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.

(a)

To determine
The frequencies of the tunnel resonates in the air.

Explanation

Given Info: The length of the tunnel is 2.00km and speed of sound in air is 343m/s .

Let us consider a standing wave is formed in the tunnel, open at both ends, one must have antinodes at each end, a node at the middle of the tunnel.

Formula for the length of the tunnel is,

L=n(λ2)

  • L is the length of the tunnel,
  • λ is the wavelength of the standing wave,
  • n is the harmonic number,

Rewrite the above relation in terms of λ .

λ=2Ln (1)

The resonance frequency of the tunnel is,

fn=vλn (2

  • fn is the frequency of the tunnel,
  • v is the speed of the sound in air,
  • λn is the wavelength of the standing wave,

Use equation (1) to rewrite equation (2) in term of fn .

fn=nv2L (3)

Conclusion:

The resonance frequency of the tunnel is,

fn=nv2L

Substitute 2

(b)

To determine
Whether it would be good to make a rule against blowing the car horn in the tunnel.

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