If two waves having amplitudes $2A$ and $A$ and same frequency and velocity,propagate in the same direction in the same phase,the resulting amplitude will be

The equations of motion for two waves traveling in the same direction are given by ${y_1} = A\sin (\omega t - kx)$ and ${y_2} = A\sin (\omega t - kx - \theta )$. The resultant amplitude of the medium particle will be

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

An observer receives waves directly from a source of sound distant $120\,m$ in a big hall. He also receives waves reflected from the mid-point of a $25\,m$ high ceiling. The wavelength of sound for constructive interference to take place between the two waves must be:

Out of the given four waves $(1), (2), (3)$ and $(4)$:
$y = a \sin(kx + \omega t)$ ......$(1)$
$y = a \sin(\omega t - kx)$ ......$(2)$
$y = a \cos(\omega t - kx)$ ......$(3)$
$y = a \cos(kx + \omega t)$ ......$(4)$
emitted by four different sources $S_1, S_2, S_3$ and $S_4$ respectively,interference phenomena would be observed in space under appropriate conditions when:

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves,$y_1(x, t) = 4 \sin(kx - \omega t)$ and $y_2(x, t) = 2 \sin(kx - \omega t + \frac{2\pi}{3})$,are (Take the angular frequency of initial waves same as $\omega$):