A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of $584 \mathrm {~Hz}$ What is the speed of sound in the air in this pipe?
A)358 m/s
B)349 m/s
C)353 m/s
D)344 m/s
E)363 m/s

Question

Quizplus · Accepted Answer

The second overtone has $n=3$. The frequency of the second overtone is given by:$$f_3=\frac{3v}{2L}$$where $v$ is the speed of sound and $L$ is the length of the pipe. Solving for $v$, we get:$$v=\frac{2Lf_3}{3}$$Substituting the given values, we get:$$v=\frac{2(0.92 \mathrm{~m})(584 \mathrm{~Hz})}{3}=353 \mathrm{~m/s}$$Therefore, the speed of sound in the air in this pipe is 353 m/s.

A Pipe That Is 0 584 Hz584 \mathrm {~Hz}584 Hz What Is the Speed of Sound in the Air in Both

A Pipe That Is 0 $584 \mathrm {~Hz}$ What Is the Speed of Sound in the Air in Both