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 string of mass $m$ and length $l$ hangs from ceiling as shown in the figure. Wave in string moves upward. $v_A$ and $v_B$ are the speeds of wave at $A$ and $B$ respectively. Then $v_B$ is

A small source of sound moves on a circle as shown in the figure and an observer is standing on $O.$ Let $n_1,\, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then

A sound absorber attenuates the sound level by $20\, dB$. The intensity decreases by a factor of

A stretched wire of length $110\,cm$ is divided into three segments whose frequencies are in ratio $1 : 2 : 3.$ Their lengths must be

A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$