A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of 584 ${~Hz}$ 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:$$f_3 = 3f_1$$where $f_1$ is the fundamental frequency. The fundamental frequency is given by:$$f_1 = \frac{v}{2L}$$where $v$ is the speed of sound and $L$ is the length of the pipe. Substituting the given values into the equation for the fundamental frequency, we get:$$f_1 = \frac{v}{2(0.92 \ m)} = 584 \ Hz$$Solving for $v$, we get:$$v = 2(0.92 \ m)(584 \ Hz) = 353 \ m/s$$

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

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