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 ..... $Hz$

Two waves represented by ${y_1} = a\sin \frac{{2\pi}}{\lambda }\left( {vt - x} \right)$ and ${y_2} = a\cos \frac{{2\pi }}{\lambda }\left( {vt - x} \right)$ are superposed. The resultant wave has an amplitude equal to

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

During propagation of a plane progressive mechanical wave incorrect statement is

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be

The phase difference between two points separated by $0.8 m$ in a wave of frequency $120 Hz$ is ${90^o}$. Then the velocity of wave will be ............ $\mathrm{m/s}$