Waves

JEE Main level, single correct, medium

101 of 142

Question 101 of 142

A closed organ pipe has a fundamental frequency of 1.5kHz1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be ((Assume that the highest frequency a person can hear is 20,000Hz20,000 Hz).

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Answer: (C) 66

For a closed organ pipe, the resonate frequency(harmonics) is an odd multiple of the fundamental frequency.
Therefore, (2n−1)f0≤20000Hz\left(2n-1\right){f}_{0}\leq 20000Hz, where n=1,2,3...n=1,2,3...
f0=1.5kHz⇒{f}_{0}=1.5kHz\Rightarrow fundamental frequency
Then, n=7n=7
The total number of overtones that can be heard is 66. (2nd{2}^{nd} harmonic to 7th{7}^{th} harmonic. )

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