The velocities of sound at the same pressure in two monatomic gases of densities ${\rho _1}$ and ${\rho _2}$ are $v_1$ and $v_2$ respectively. ${\rho _1}/{\rho _2} = 2$, then the value of $\frac{{{v_1}}}{{{v_2}}}$ is

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 ..... $Hz$

The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

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

Beats are produced by two waves $y_1 = a\, sin\, (1000\, \pi t)$ and $y^2 = a\, sin\, (998\, \pi t)$ The number of beats heard per second is

A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is   .... $Hz$