Question

An organ pipe open at both ends has two successive harmonics with frequencies of 220 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 343 m/s in air.

Answer 1

The length is
`l = 8.6 \ m`

Step-by-step explanation:

From the question we are told that

The frequencies of the two successive harmonics are
`f_1 = 220 \ Hz` ,
`f_2 = 240 \ Hz`

The speed of sound in the air is
`v_s = 343 \ m/s`

Generally the frequency of a given harmonic is mathematically represented as

`f_n = (n v )/(2l)`

Here n defines the position of the harmonics

Now since the position of both harmonic is not know but we know that they successive then we can represented them mathematically as

`220 = (n v)/(2l)`

and

`240 = ((n+1) v)/(2l)`

So

`((n + 1 ) v)/(2l) - (n v)/(2l) = 240-220`

=>
`(v)/(2l) = 20`

=>
`l = 8.6 \ m`