Fifth overtone of an open pipe of length $L_0$ is in unison with the fifth overtone of the pipe closed at one end of length $L_c$.
The ratio $L_0$ to $L_c$ is

The lengths of the two pipes open at both ends are L and $(L + L_1)$. If they are sounded together, the beat frequency will be
($v$ = velocity of sound in air)

The number of waves counted by an observer on the sea-coast in one minute is 54. If the wavelength of the waves is $5\ \text{m}$ then the velocity of the waves in $\text{m/s}$ will be

When a dipole placed parallel to electric field is rotating through $\pi^c$, the work done is W. The work done in rotating the dipole through $\left(\dfrac{\pi}{3}\right)^c$ is
($\cos 0^\circ = 1$, $\cos 60^\circ = \dfrac{1}{2}$, $\cos 180^\circ = -1$)