Example from Physics, 14.4 Sound Interference and Resonance

Finding the Length of a Tube for a Closed-Pipe Resonator

If sound travels through the air at a speed of 344 m/s, what should be the length of a tube closed at one end to have a fundamental frequency of 128 Hz?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The length L can be found by rearranging the equation $f_{n} = n \frac{v}{4 L}$ .
2
Solution
(1) Identify knowns.
- The fundamental frequency is 128 Hz.
- The speed of sound is 344 m/s.
(2) Use $f_{n} = n \frac{v_{w}}{4 L}$ to find the fundamental frequency (n = 1).

$f_{1} = \frac{v}{4 L}$
14.14

(3) Solve this equation for length.

$L = \frac{v}{4 f_{1}}$
14.15

(4) Enter the values of the speed of sound and frequency into the expression for L.

$L = \frac{v}{4 f_{1}} = \frac{344 m/s}{4 (128 Hz)} = 0.672 m$
14.16

0 of 2 steps open

How did it go?

Strategy

Solution