1
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Question

How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound =340 ms−1

A
12
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B
18
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C
24
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D
30
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Solution

The correct option is C 24=f=v4l=3404×0.2=3400.8=425 HZ This is in the audible range. (20 Hz to 20000 Hz) The next overtones are 3f, 5f . . . . which are present in the pipe Let there be n harmonics nf≤20000 n≤20000425=47 The nthharmonic present in the pipe is 19975. So the harmonics are 425, 1275, . . . . 19975 Number of terms in this A.P 19975=425+(n−1)850=425+850n−85019975+425=850n400=850n∴n=20400850=24 Ans: 24

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