Question

When we clap our hands, the sound produced is best described by
(a) $p=p_0\sin \left(kx-\omega t\right)$

(b) $p=p_0\sin kx\cos \omega t$

(c) $p=p_0\cos kx\sin \omega t$

(d) $p=\sum p_{0n}\sin \left(k_{n}x-{\omega }_{n}t\right)$.

Here p denotes the change in pressure from the equilibrium value.

Answer 1

(d) $p=\sum p_{0n}\sin \left(k_{n}x-{\omega }_{n}t\right)$.

When we clap, there is a change in pressure, which sets a disturbance and forms a wave. However, this variation is not uniform every time we clap (unlike in the case of a sound wave). Hence, we sum up all the disturbances.