Two cars $A$ and $B$ are moving in the same direction with speeds $36\,km/hr$ and $54\,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency $1000\,Hz$ and the speed of sound in air is $340\,m/s$, the frequency of sound received by the driver of car $B$ is .................. $\mathrm{Hz}$

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 $y = a\,\sin \,\left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is

Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t.$  Number of beats produced per minute is

When a string is divided into three segments of length $l_1,\,l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1,\,v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is

Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be