Two waves have the same amplitude $A$ and the same frequency $\omega$. If the phase difference between them is $\pi / 2$,what are the resultant amplitude and the resultant frequency when they superimpose at a point?

The displacement of a particle executing periodic motion is given by :
$y = 4 \cos^2(t/2) \sin(1000t)$
This expression may be considered to be a result of the superposition of

Two pulses in a stretched string whose centres are initially $8 \ cm$ apart are moving towards each other as shown in the figure. The speed of each pulse is $2 \ cm/s$. After $2 \ seconds$,the total energy of the pulses will be

Two sources of sound $A$ and $B$ produce waves of $350 Hz$,and they vibrate in the same phase. $A$ particle $P$ is vibrating under the influence of these two waves. If the amplitudes at point $P$ produced by the two waves are $0.3 mm$ and $0.4 mm$,what will be the resultant amplitude of the point $P$ when $AP - BP = 25 cm$ and the velocity of sound is $350 m/s$?

The similarity between sound waves and light waves is:

Two loudspeakers $L_1$ and $L_2$,driven by a common oscillator and amplifier,are arranged as shown. The frequency of the oscillator is gradually increased from zero,and the detector at $D$ records a series of maxima and minima. If the speed of sound is $330 \, m/s$,then the frequency at which the first maximum is observed is .... $Hz$.