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Question

The frequency of the fourth harmonic of an organ pipe is 33 Hz less than the frequency of the fifth harmonic of the same organ pipe. Find the difference in wavelengths for the given two cases. Neglect end corrections.
[speed of sound in air =330 m/s]

A
60 cm
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B
50 cm
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C
40 cm
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D
30 cm
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Solution

The correct option is B 50 cm
As there is fourth and fifth harmonics, therefore, the organ pipe is open because the closed organ pipe doesn't allow even harmonics.
According to question,
f4=f533
4v2l=5v2l33
v2l=33
l=v2×33=33066=5 m
Now, wavelength for fourth harmonic,
λ=2ln
[ f=nv2l and v=λf ]
λ4=2×54=2.5 m
Similarly, for fifth harmonic,
λ5=2 m
So,
Δλ=λ4λ5=2.52=0.5 m=50 cm

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