$A$ 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 $= 320 \,m/s$)

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

$A$ rod of length $L$ and negligible mass is suspended by two identical strings $AB$ and $CD$ as shown in the figure. $A$ mass $M$ is suspended from point $O$ which is at a distance $x$ from $B$. If the frequency of the first harmonic of $AB$ is equal to the frequency of the second harmonic of $CD$,then the value of $x$ is

$A$ wave pulse on a string has the dimensions shown in the figure. The wave speed is $v = 1 \, cm/s$. If point $O$ is a free end,what is the shape of the wave at time $t = 3 \, s$?

At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points $P$, $Q$ and $R$ on the string?

An air column in a tube $32 \,cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 \,cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):