An organ pipe close to one another fundamental frequency of 1500 hertz maximum number of overtime generated by the sides is the normal person can hear
Answers
The maximum number of overtone generated by the pipe that the normal person can hear is 6.
Explanation:
The fundamental frequency of an organ pipe is given as, f’ = v/4L = 1500Hz
We know that the audibility range for a normal person is 20 Hz – 20,000 Hz, so the critical hearing frequency of a person will be “f” = 20,000 Hz
Also, in a closed pipe vibration, the nth normal mode of the frequency of vibration is given by the relation,
f = [2n-1]* [v/4L] ….. [where n is an integer 0,1,2,3,…..]
⇒ 20,000 = [2n - 1] * 1500 ...... [on substituting the given values]
⇒ 2n - 1 = 20,000/1500
⇒ 2n – 1 = 13.33 ≈ 13
⇒ 2n = 13 + 1
⇒ n = 14/2
⇒ n = 7
Thus, we know that in a closed pipe organ,
The maximum no. of overtones possible that a normal person can hear is given by,
= [The no. of mode frequency of vibration] – 1
= n - 1
= 7-1
= 6
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