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

Answer:

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

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

$f=\dfrac{nv}{2L}$

For 550 Hz,

$550=\dfrac{n\times340}{2L}$...(I)

For 650 Hz,

$650=\dfrac{(n+1)\times340}{2L}$...(II)

From equation (I) and (II)

$550-650=\dfrac{340}{2L}-\dfrac{340}{L}$

$L=\dfrac{340}{2\times100}$

$L=1.7\ m$

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

Using formula of  fundamental frequency

$=f=\dfrac{n\lambda}{2L}$

put the value of L

$f=\dfrac{1\times340}{2\times1.7}$

$f=100\ Hz$

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