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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 595HzGiven: 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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