Two tuning forks $A$ and $B$ lying on opposite sides of observer $O$ and of natural frequency $80 Hz$ move with velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$ relative to stationary observer $O$. Fork $A$ moves away from the observer while the fork $B$ move towards him. A wind with a speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ is blowing towards fork $A$ from $B\mathit{.}$ Find the beat frequency measured by the observer in $Hz.$ [Take speed of sound in air as $340 \mathrm{m} {\mathrm{s}}^{-1}$ ]

A copper wire is held at the two ends by rigid supports. At $30°\mathrm{C}$ the wire is just taut, with negligible tension. The speed of transverse waves in this wire at $10°\mathrm{C}$ is:

$\left(\mathrm{\alpha }=1.7\times {10}^{-5}°\mathrm{C},\mathrm{Y}=1.3\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2, \mathrm{d}=9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3\right).$

The transverse displacement $y\left(x,t\right)$ of a wave on a string is given by $y\left(x,t\right)=e^{-\left(a{x}^2+b{t}^2+2\sqrt{ab}xt\right)}$ This represents a

Three consecutive flash photographs of a travelling wave on a string are reproduced in the figure here. The following observations are made. Mark the one which is correct. (Mass per unit length of the string $=3 \mathrm{g} {\mathrm{cm}}^{-1}$)

If vibrations of a string are to be increased by a factor of two, then tension in the string must be made