   Chapter 14, Problem 58P

Chapter
Section
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.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Lysine does not cure herpes infections. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

Velocity is a(n) ___ quantity. (2.2)

An Introduction to Physical Science

What is an epigenetic change?

Introduction to General, Organic and Biochemistry 