Two identical sounds $S_1$ and $S_2$ reach at a point $P$ in phase. The resultant loudness at point $P$ is $n\,\, dB$  higher than the loudness of $S_1$. The value of $n$ is

A wave travelling along the $x-$ axis is described by the equation $y\ (x, t )\ =\ 0.005\ cos\ (\alpha x - \beta t )$ . If the wavelength and the time period of the wave in $0.08\ m$ and $2.0\ s$ respectively then $\alpha $ and $\beta $ in appropriate units are

The displacement $y$ of a wave travelling in the $x-$ direction is given by $y = {10^{ - 4}}\sin \left( {600t - 2x+\frac{\pi }{3}} \right)$ metre, where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $ms^{-1}$, is

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave

The speed of sound in oxygen $(O_2)$ at a certain temperature is $460\, ms^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be ............. $\mathrm{m/s}$  (assume both gases to be ideal)

Two waves represented by, $y_1 = 10\,sin\, 200\pi t$ , ${y_2} = 20\,\sin \,\left( {2000\pi t + \frac{\pi }{2}} \right)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is