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 interfering waves have the same wavelength,frequency,and amplitude. They are traveling in the same direction but are $90^o$ out of phase. Compared to the individual waves,the resultant wave will have the same.

The equations of two waves are given by
$y_{1}=5 \sin 2 \pi(x-v t) \, cm$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \, cm$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$.

Three coherent waves of equal frequencies having amplitudes $10 \, \mu m$,$4 \, \mu m$,and $7 \, \mu m$ respectively,arrive at a given point with successive phase differences of $\pi / 2$. The amplitude of the resulting wave in $\mu m$ is given by

Four independent waves are represented by the following equations. Which of these equations represent the phenomenon of interference?
$Y_1 = a_1 \sin \omega t$
$Y_2 = a_2 \sin \omega t$
$Y_3 = a_3 \cos \omega t$
$Y_4 = a_4 \sin (\omega t + \frac{\pi}{3})$

When two sound waves with a phase difference of $\pi / 2$,and each having amplitude $A$ and frequency $\omega$,are superimposed on each other,then the maximum amplitude and frequency of the resultant wave is: