Assignment

A transverse sine wave moves along a string in the positive $x$-direction at a speed of $20 \mathrm{cm} {\mathrm{s}}^{-1}.$ The wavelength of the wave is $1 \mathrm{m}$ and its amplitude is $10 \mathrm{cm}.$ The snapshot of the wave is shown in the figure. The acceleration and velocity of point $P$ whose displacement at this instant is $5 \mathrm{cm}$ are ${\overrightarrow{a}}_p$ and ${\overrightarrow{v}}_p$ respectively. Then

In a resonance tube experiment with a closed organ pipe of length $130 \mathrm{cm}$, the frequency of tuning fork used is $340 \mathrm{Hz}.$ Take end connection as $5 \mathrm{cm}.$ If water is poured into the pipe, then the correct statement(s) is/are (speed of sound in air $=340 \mathrm{m} {\mathrm{s}}^{-1}$).

The equation of a standing wave produced on a string fixed at both ends at $x=0$ and $x=L$ respectively is $y=\left(0.8 \mathrm{cm}\right)\sin \left[\left(0.314{ \mathrm{cm}}^{-1}\right)x\right]$ $\cos \left[\left(600\pi {\mathrm{s}}^{-1}\right)t\right].$ Choose the correct statement(s)

A standing wave given by the equation, $S=S_0$ $sinkx.\cos wt$ is maintained in a homogeneous rod with cross-sectional area $A$ and density $d$, where $S$ represents displacement of a particle from its mean position. Then select the correct statement(s)

A wave disturbance in a medium is described by $y\left(x, t\right)=0.04\cos \left(50\pi t+\frac{\pi }{2}\right)\cos \left(10\pi x\right)$, where $x$ and $y$ are in meters and$\text{'}f\text{'}$ is in seconds.
(i) Displacement node occurs at $x=0.15 \mathrm{m}$
(ii) At $t=\frac{1}{50} \mathrm{s}$, particle at $x=0.20 \mathrm{m}$ will be moving with speed $2\pi \mathrm{m} {\mathrm{s}}^{-1}$
(iii) At $t=\frac{1}{100} \mathrm{s}$, particle at $x=\frac{1}{15} \mathrm{m}$ will beat a displacement of $0.02 \mathrm{m}$ from it's own mean position
(N) At $t=\frac{3}{100} \mathrm{s}$, particle at $x=\frac{1}{15} \mathrm{m}$ will beat a displacement of $0.02 \mathrm{m}$ from it's own mean position

A taut string (fixed at both ends) vibrates in its $m^{th}$ overtone. The minimum distance between two points which is vibrating with maximum possible amplitude $\left(A\right)$ and half of the maximum possible amplitude $\left(\frac{A}{2}\right)$ respectively is$\text{'}d\text{'}.$ Then length$\text{'}L\text{'}$ of the string is

Three waves are propagating in same direction and pass through a point simultaneously. The variation of electric field with time is as

$E_1=E_0\cos \omega t, E_2=2E_0\sin \omega t$ and
$E_3=5E_0\cos \left(\omega t+53°\right);$ and intensity due to
first wave at that point is $I_0.$ Then

A string of length $50 \mathrm{cm}$ and mass $2.5 \mathrm{g}$ is fixed at both ends with a tension of $52 \mathrm{N}.$ A closed organ pipe has length $85 \mathrm{cm}.$ The string vibrates in its second overtone and the air column in the pipe in its first overtone. Neglect the end correction in the pipe and the speed of sound in air is $340 \mathrm{m} {\mathrm{s}}^{-1}.$ Then