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 plan wave of sound traveling in air is incident upon a plan surface of a liquid. The angle of incidence is $60^o$. The speed of sound in air is $300\ m/s$ and in the liquid it is $600\ m/s$. Assume Snell's law to be valid for sound waves 

Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t.$  Number of beats produced per minute is

A train whistling at constant frequency is moving towards a station at a constant speed $V$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t (Fig.)$ . Identify the expected curve

The diagram shows snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. Direction of propagation of wave is

Fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is