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Question

For an organ pipe, resonance frequencies are observed at 425Hz and 765Hz. The speed of sound in air is 340m/s.Find a resonance frequency between these two frequencies

A
595Hz
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B
575Hz
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C
535Hz
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D
605Hz
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Solution

The correct option is A 595Hz

Given:

Speed of sound= 340m/sec

Let us assume that the organ pipe is closed. Then the consecutive frequencies can be written as

nfo,(n+2)fo,(n+4)fo

Where, fo is the fundamental frequency

The first consecutive frequency can be written as,f1 425=nfo …(1)

The second consecutive frequency can be written as, f2=(n+2)fo ….(2)

The third consecutive frequency can be written as,f3 765=(n+4)fo …(3)

Taking ratio of equation (1), (2) and (3), we get, n=5

Putting this value in equation (1), we get,fo=85

Hence, fundamental frequency is 85Hz

Putting this value in equation (2)

f2=(5+2)85

f2=595

Therefore, the frequency between the two frequency is 595 Hz

Correct answer (a)


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