Two waves of frequency $f$ and amplitude $a$ superimpose with each other. The total intensity is directly proportional to

Two sound waves each of wavelength $\lambda$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\frac{\lambda}{4}$, the amplitude of the resultant wave at point $Q$ is $[\sin \frac{\pi}{2} = 1, \cos \frac{\pi}{2} = 0]$

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.

The amplitude of the resultant wave produced by the superposition of two waves $y_1 = A_1 \sin(wt - \beta_1)$ and $y_2 = A_2 \sin(wt - \beta_2)$ is:

Two waves are propagating along a taut string that coincides with the $x$-axis. The first wave has the wave function $y_1 = A \cos[k(x - vt)]$ and the second has the wave function $y_2 = A \cos[k(x + vt) + \phi]$.

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: