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 two waves represented by $y_1 = a\,sin(\omega\,t)$ and $y_2 = b\, cos\, (\omega\, t)$ have a phase difference of

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

When a wave travels in a medium, the particle displacement is given by : $y = asin\, 2 \pi \,(bt -cx)$, where $a, b$ and $c$ are constants. The maximum particle velocity will  be twice the wave velocity if

The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06$ $sin\, (2\pi x /3)\, cos\, (120\, \pi t)$. All the points on the string between two consecutive nodes vibrate with

A string of mass $100\, gm$ is clamped between two rigid support. A wave of amptitude $2\, mm$ is generated in string. If angular frequency of wave is $5000\, rad/s$ then total energy of the wave in string is ..... $J$