Beats are produced by two waves $y_1 = a\, sin\, (1000\, \pi t)$ and $y^2 = a\, sin\, (998\, \pi t)$ The number of beats heard per second is

A string fixed at one end is vibrating in its second overtone. The length of the string is $10\  cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9\  meters$ and $25\  meters$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

A pulse on a string is shown in the figure. $P$ is particle of the string. Then state which of the following is incorrect