Question

You have a long pipe closed at one end and an electronic buzzer with which you can dial in different single frequency sounds. When you hold the buzzer near the end of the pipe, transmitting sound down the pipe, you determine that standing waves are established at frequencies of 66, 110, and 154 Hz. The frequency of 66 Hz is not necessarily the fundamental frequency. Determine the length of the pipe if the speed of sound in air is 343 m/s.

Answer 1

3.89m

Step-by-step explanation:

To find the length of the pipe you can use the formula for the modes of the pipe with a closed end:

`f=((2n+1)v_s)/(4L)`

n: mode of frequency

vs : sound speed = 343m/s

L: length of the pipe

by taking the difference between two consecutive modes you obtain:

`f_n-f_(n-1)=((2n+1)v_s)/(4L)-((2(n-1)+1)v_s)/(4L)=(v_s)/(2L)`

by using two consecutive frequencies in the previous expression and replacing you get:

`110-66=44=(v_s)/(2L)\\\\L=(v_s)/(2(44)/s)=(343m/s)/(88/s)=3.89m`

hence, the length of the pipe is 3.89m