$A$ pipe closed at one end has a length of $0.8 \,m$. At its open end, a $0.5 \,m$ long uniform string is vibrating in its $2^{nd}$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \,N$ and the speed of sound is $320 \,m/s$, what is the mass of the string (in $\,g$)?

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?

$A$ transverse sinusoidal wave of amplitude $a,$ wavelength $\lambda,$ and frequency $n$ is travelling on a stretched string. The maximum speed of any point on the string is $v/10,$ where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ m/s,$ then $\lambda$ and $n$ are given by:

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

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Fill in the blanks:
$(i)$ If the fundamental frequency of a given closed pipe is $50 \ Hz$,then the frequency for the second overtone is ...... .
$(ii)$ The speed of sound in air at $STP$ is ...... .
$(iii)$ In the case of sound waves,in order to experience beats quite clearly,the value of the beat frequency $|f_1 - f_2|$ should not be greater than ...... .