The resultant amplitude of waves ${y_1} = a \sin \left( \omega t + \frac{\pi}{3} \right)$ and ${y_2} = a \sin \omega t$ is:

Two waves represented by $y_1 = 10 \sin(2000 \pi t + 2x)$ and $y_2 = 10 \sin(2000 \pi t + 2x + \frac{\pi}{2})$ are superposed at any point at a particular instant. The resultant amplitude is ..... $unit$.

Three harmonic waves having equal frequency $v$ and same intensity $I_{0}$,have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed,the intensity of the resultant wave is close to

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 $............. \text{ cm}$.

When two light waves each of amplitude $A$ and having a phase difference of $\frac{\pi}{2}$ are superimposed,the amplitude of the resultant wave is:

Two simple harmonic waves having equal amplitudes of $8\,cm$ and equal frequency of $10\,Hz$ are moving along the same direction. The resultant amplitude is also $8\,cm$. The phase difference between the individual waves is $..................$ degree.