Consider an element of a stretched string along which a wave travels. During its transverse oscillatory motion, the element passes through a point at $y=0$ and reaches its maximum at $y= y_{\mathrm{m}}$. Then, the string element has its maximum

A massless rod $BD$ is suspended by two identical massless strings $AB$ and $CD$ of equal lengths. A block of mass $‘m’$ is suspended point $P$ such that $BP$ is equal to $x$, if the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of $x$ is:

A transverse sinusoidal wave moves along a string in the positive $x$ -direction at a speed of $10 \mathrm{cm} {\mathrm{s}}^{-1}$. The wavelength of the wave is $0.5 \mathrm{m}$ and its amplitude is $10 \mathrm{cm}.$ At a particular time $t$ the snap-shot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \mathrm{cm}$ is

Figure:

A $20 \mathrm{cm}$ long string, having a mass of $1.0 \mathrm{g}$, is fixed at both ends. The tension in the string is $0.5 \mathrm{N}$. The string is set into vibration using an external vibrator of frequency $100 \mathrm{Hz}$. Find the separation (in $\mathrm{cm}$) between the successive nodes on the string.

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation $\mathrm{y}\left(\mathrm{x},\mathrm{t}\right)=0.01 \mathrm{m} \sin \left[\left(62.8 {\mathrm{m}}^{-1}\right)\mathrm{x}\right] \cos \left[\left(628 {\mathrm{s}}^{-1}\right)\mathrm{t}\right].$ Assuming $\mathrm{\pi }=3.14,$ the correct statement is (are)

A block $M$ 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 ${\mathrm{\lambda }}_0$ is produced at point $O$ on the rope. The pulse takes time $T_{\mathit{O}\mathit{A}}$ to reach point $A$. If the wave pulse of wavelength ${\mathrm{\lambda }}_0$ is produced at point $A$ (Pulse $2$) without disturbing the position of $M$ it takes time $T_{\mathit{A}\mathit{O}}$ to reach point $O$. Which of the following options is/are correct.