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 $v = 300 \, m/s$)

$A$ wave disturbance in a medium is described by $y(x, t) = 0.02 \cos(50 \pi t + \frac{\pi}{2}) \cos(10 \pi x)$,where $x$ and $y$ are in metres and $t$ is in seconds.

“Stationary waves” are so called because in them

The equation of a stationary wave is $y = 20 \sin(\pi x) \cos(\omega t)$,where $x$ and $y$ are in meters and $t$ is in seconds. The distance between a node and its adjacent antinode is (in $\text{ cm}$)

The pattern of standing waves formed on a stretched string at two instants of time is shown in the figure. The velocity of the two waves superimposing to form stationary waves is $360 \ m/s$ and their frequencies are $256 \ Hz$.
$(a)$ Calculate the time at which the second curve is plotted.
$(b)$ Mark nodes and antinodes on the curve.
$(c)$ Calculate the distance between $A^{\prime}$ and $C^{\prime}$.

The transverse displacement of a string (clamped at both ends) is given by $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \; m$ and its mass is $3.0 \times 10^{-2} \; kg$. Answer the following:
$(a)$ Does the function represent a travelling wave or a stationary wave?
$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength,frequency,and speed of each wave?
$(c)$ Determine the tension in the string.