A tuning fork of frequency $340\, Hz$ is sounded above an organ pipe of length $120\, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is …. $cm$ (speed of sound in air $= 340 \,m/s$)

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is  …. $N$

A steel rod $100\,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel …… $km/sec$

A transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement.

A block $\mathrm{M}$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse $1$ ) of wavelength $\lambda_0$ is produced at point $O$ on the rope. The pulse takes time $T_{O A}$ to reach point $A$. If the wave pulse of wavelength $\lambda_0$ is produced at point $A$ (Pulse $2$) without disturbing the position of $M$ it takes time $T_{A 0}$ to reach point $O$. Which of the following options is/are correct?

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[$A$] The time $\mathrm{T}_{A 0}=\mathrm{T}_{\mathrm{OA}}$

[$B$] The velocities of the two pulses (Pulse $1$ and Pulse $2$) are the same at the midpoint of rope.

[$C$] The wavelength of Pulse $1$ becomes longer when it reaches point $A$.

[$D$] The velocity of any pulse along the rope is independent of its frequency and wavelength.