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 pulses on a string approach each other at speeds of $1 \ m/s$. What is the shape of the string at $t = 3 \ s$ :-

Two waves of the same frequency and same amplitude $a$ are superimposed. If the resultant amplitude is also $a$,what is the phase difference between the two waves?

Two waves of amplitudes $A_1$ and $A_2$ respectively are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is $9 : 4$. The value of $A_2 / A_1$ is [Assume $A_1 > A_2$]

Sound waves are passing through two routes—one in a straight path and the other along a semicircular path of radius $r$—and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is $v$, then frequencies of resultant waves of maximum amplitude will be integral multiples of

$A$ person standing at a distance of $6\, m$ from a source of sound receives sound waves in two ways: one directly from the source and the other after reflection from a rigid boundary,as shown in the figure. The maximum wavelength for which the person will receive maximum sound intensity is .... $m$.