$A$ progressive wave travelling in the positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by

If in a stationary wave the amplitude corresponding to an antinode is $4 \,cm$,then the amplitude corresponding to a particle of medium located exactly midway between a node and an antinode is ........... $cm$.

The given diagram shows a detector placed between a transmitter of sound waves and a metal plate. At three adjacent points,$R, S$ and $T$,the meter shows zero intensity. Which of the following is the frequency of the emitted wave in $Hz$? (Take the velocity of sound as $v = 300 \, m/s$)

Standing waves are produced in a $10 \; m$ long stretched string. If the string vibrates in $5$ segments and the wave velocity is $20 \; m/s$,the frequency is ... $Hz$.

Two waves are approaching each other with a velocity of $20 \ m/s$ and frequency $n$. The distance between two consecutive nodes is

Two progressive waves $Y_{1} = \sin 2\pi(\frac{t}{0.4} - \frac{x}{4})$ and $Y_{2} = \sin 2\pi(\frac{t}{0.4} + \frac{x}{4})$ superpose to form a standing wave. $x, Y_{1}$ and $Y_{2}$ are in $SI$ units. The amplitude of the particle at $x = 0.5 \ m$ is: (Given: $\sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}}$)