Two waves represented by $y_1 = 10 \sin(200\pi t)$ and $y_2 = 20 \sin(200\pi t + \pi/2)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is:

Three waves of equal frequency having amplitudes $10 \,\mu m, 4 \,\mu m$ and $7 \,\mu m$ arrive at a given point with successive phase difference of $\frac{\pi}{2}$. The amplitude of the resulting wave in $\mu m$ is given by

The displacement equations of two interfering waves are given by
$y_1 = 10 \sin \left(\omega t + \frac{\pi}{3}\right) \text{ cm}$
$y_2 = 5[\sin (\omega t) + \sqrt{3} \cos \omega t] \text{ cm}$ respectively.
The amplitude of the resultant wave is $............. \text{ cm}$.

Two waves have equations $x_1 = a \sin(\omega t + \phi_1)$ and $x_2 = a \sin(\omega t + \phi_2)$. If in the resultant wave the frequency and amplitude remain equal to the amplitude of the superimposing waves,the phase difference between them is ........

Two waves $Y_1 = A_1 \sin(\omega t - \beta_1)$ and $Y_2 = A_2 \sin(\omega t - \beta_2)$ superimpose to form a resultant wave whose amplitude is

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: