An organ pipe closed at one end has fundamental frequency of 1500 Hz. The maximum number of overtones generated by this pipe which a normal person can hear is

An organ pipe closed at one end has fundamental frequency of 1500 Hz.

1.	An organ pipe closed at one end has fundamental frequency of 1500 Hz. The maximum number of overtones generated by this pipe which a normal person can hear is
Answer» 14 13 6 9 Solution :In case of closed pipe, `f = (2n + 1) f _(1)` (Where `f _(1)=` fundamental frequency, `2n +1= ` order of harmonic, `n = 0,1,2,3,…=` order of overtone) Note : If we take `f =(2n -1) f _(1),`then `2n -1=` order of harmonic, `n = 1,2,3…., n-1 =` order of overtone) Here `f = 20000 HZ and f _(1) = 1500 Hz and so 20000 = (2n +1) xx 1500` `therefore 2n +1 = 13.33` `therefore 2n +1 =13 (because ` here (2n +1) is less than 15 and an odd integer) `therefore n =6` `6^(th)` overtone is the MAXIMUM order os overtone (or highest overtone) that can be heard in this case. (Because if we take n = 7 then (2n +1) `f _(1) = 15 xx 1500 =22500` which would be GREATER than 20000 Hz and so it would be wrong).