Question

Two adjacent natural frequencies of an organ pipe are AMT determined to be 550 Hz and 650 Hz. Calculate (a) the M fundamental frequency and (b) the length of this pipe.

Answer 1

The fundamental frequency and length of the pipe are 100 Hz and 1.7 m.

Step-by-step explanation:

Given that,

Frequency f = 550 Hz

Frequency f' = 650 Hz

We know that,

AMT pipe is open pipe.

(b). We need to calculate the length of the pipe

Using formula of organ pipe

`f=(nv)/(2L)`

For 550 Hz,

`550=(n*340)/(2L)`...(I)

For 650 Hz,

`650=((n+1)*340)/(2L)`...(II)

From equation (I) and (II)

`550-650=(340)/(2L)-(340)/(L)`

`L=(340)/(2*100)`

`L=1.7\ m`

(a). We need to calculate the fundamental frequency for n = 1

Using formula of fundamental frequency

`=f=(n\lambda)/(2L)`

put the value of L

`f=(1*340)/(2*1.7)`

`f=100\ Hz`

Hence, The fundamental frequency and length of the pipe are 100 Hz and 1.7 m.