   Chapter 14, Problem 59P

Chapter
Section
Textbook Problem

A pipe open at both ends has a fundamental frequency of 3.00 × 102 Hz when the temperature is 0°C. (a) What is the length of the pipe? (b) What is the fundamental frequency at a temperature of 30.0°C?

(a)

To determine
The length of the pipe open at both ends.

Explanation

Given Info: A pipe is open at both the ends

In the fundamental mode for an open pipe, the length of the pipe is,

L=λ2 (1)

• λ is the fundamental wavelength.
• L is the length of the pipe

The relation between velocity and frequency is,

v=λf

• v is the speed of the sound in air.
• f is the fundamental frequency.

Rewrite the above expression in terms of λ .

λ=vf (2)

Substitute equation (2) in (1)

L=v2f

Formula to calculate the length of the pipe is,

L=v2f

Substitute 331m/s for v and 3

(b)

To determine
The fundamental frequency at a temperature of 30°C .

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