Question

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range (20-20,000 Hz). Speed of sound in air = $340m{s}^{-1}$.

Answer 1

Let the length will be I.

Here given that,

V=340 m/s

and n =20 Hz

Here $\frac{\lambda }{2}=2I$

We know, $v=n\lambda$

$\Rightarrow I=\frac{V}{2\times n}=\frac{340}{2\times 20}$

$=\frac{34}{4}=8.5cm$

(for maximum wavelength the frequency is minimum)