Question

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

Answer 1

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  

Hope this is helpful!!!!!