Question

Two adjacent natural frequencies of an organ pipe are determined to be 986 Hz and 1102 Hz. (Assume the speed of sound is 343 m/s.) (a) Calculate the fundamental frequency of this pipe. (b) Calculate the length of this pipe.

Answer 1

Answer:

The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.

Explanation:

Given that,

First frequency = 986 Hz

Second frequency = 1102 Hz

We need to calculate the length of the pipe

Using formula of length

$\Delta f=f_{2}-f_{1}=\dfrac{nv}{2L}$

Put the value into the formula

$1102-986=\dfrac{1\times343}{2\times L}$

$L=\dfrac{343}{2\times116}$

$L=1.48\ m$

We need to calculate the fundamental frequency of this pipe

$f_{1}=\dfrac{nv}{2L}$

Put the value into the formula

$f_{1}=\dfrac{1\times343}{2\times1.48}$

$f_{1}=115.8\ Hz$

Hence, The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.