The ratio of the velocity of sound in hydrogen $(\gamma = 7/5)$ to that in helium $(\gamma = 5/3)$ at  the same temperature is

A person speaking normally produces a sound intensity of $40\, dB$ at a distance of $1\, m$. If the threshold intensity for reasonable audibility is $20\,dB$, the maximum distance at which he can be heard clearly is ..... $m$

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 of mass $2.5\, kg$ under some tension. The length of the stretched string is $20\, m$. If the transverse jerk produced at one end of the string takes $0.5\, s$ to reach the  other end, tension in the string is .... $N$

A massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. A block of mass $m$ is suspended from point $ O $ such that $BO$ is equal to $’x’$. Further, it is observed that the frequency of $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to $2^{nd}$ harmonic frequency in $CD$. Then, length of $BO$ is

The equation of a stationary wave is

$y = 0.8\,\cos \,\,\left( {\frac{{\pi x}}{{20}}} \right)\,\sin \,200\,\pi t$

where $x$ is in $cm$ and $t$ is in $sec$ . The separtion between consecutive nodes will be .... $cm$