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)

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 are $0.08 \,\,m$ and $2.0\,\,s,$  respectively, then $\alpha $ and $\beta $ in appropriate units are

A string with a mass density of $4\times10^{-3}\, kg/m$ is under tension of $360\, N$ and is fixed at both ends. One of its resonance frequencies is $375\, Hz$. The next higher resonance frequency is $450\, Hz$. The mass of the string is

For waves propagating in a medium, identify the property that is independent of the others

Three sound waves of equal amplitudes have frequencies $(f-1 ), f, (f+ 1)$. They superpose to give beats. The number of beats produced per second will be:

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