$A$ pipe open at one end has length $0.8 \,m$. At the open end of the tube, a string $0.5 \,m$ long is vibrating in its $1^{\text{st}}$ overtone and resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \,N$, what is the mass of the string (in $\,g$)? (Speed of sound $= 320 \,m/s$)

$A$ parallel beam of light is incident on a tank filled with water up to a height of $61.5 \,mm$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \,MHz$ are sent along the length of the water column using a transducer placed at the top and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? (Take the speed of sound in water to be $1500 \,m/s$)

The wavelength of light in the visible part $(\lambda_V)$ and for sound $(\lambda_S)$ are related as:

Which of the following graphs is/are correct?

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. The maximum intensity produced at $D$ is given by

The displacement of a particle in a string stretched in the $X$ direction is represented by $y$. Among the following expressions for $y$,which ones describe wave motion?