Question

An organ pipe enclosed 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 : a) 6 b)11 c)9 d)13.

Answer 1

Answer on Question #38005, Physics, Acoustics

Question:

An organ pipe enclosed at one end has fundamental frequency of $1500\,\mathrm{Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is: a) 6 b) 11 c) 9 d) 13.

Answer:

A human ear usually hear sound in range from $20\,\mathrm{Hz}$ to $20\,\mathrm{kHz}$. If an organ pipe has the fundamental frequency of $f_0 = 1500\,\mathrm{Hz} = 1.5\,\mathrm{kHz}$, overtones have frequencies $f_n = nf, n > 1$. Thus, the number of overtones which a normal person can hear can be estimated as

$$N = \left[ \frac{20\,\mathrm{kHz}}{1.5\,\mathrm{kHz}} \right] = 13,$$

where $[x]$ means the integer part of $x$. So, the right answer is d) 13.