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

The velocities of sound at the same pressure in two monatomic gases of densities ${\rho _1}$ and ${\rho _2}$ are $v_1$ and $v_2$ respectively. ${\rho _1}/{\rho _2} = 2$, then the value of $\frac{{{v_1}}}{{{v_2}}}$ is

A train is moving towards a stationary observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?

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 $t$. 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

Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series.  The fundamental frequency of the new pipe so obtained will be