A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is

A musical instrument ' $P$ ' produces sound waves of frequency ' $n$ ' and amplitude ' $A$ '. Another musical instrument ' $Q$ ' produces sound waves of frequency $\frac{\mathrm{n}}{4}$. The waves produced by ' $P$ ' and ' $Q$ ' have equal energies. If the amplitude of waves produced by ' $P$ ' is ' $A_P$ ', the amplitude of waves produced by ' $Q$ ' will be

A sonometer wire is in unison with a tuning fork of frequency ' $n$ ' when it is stretched by a weight of specific gravity ' $d$ '. When the weight is completely immersed in water, ' $x$ ' beats are produced per second, then

The equations of two waves are given as

$$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned}$$

If amplitude and time period of resultant wave is same as the individual waves, then $\left(\phi_1-\phi_2\right)$ is