Power Transmitted by a Wave on a String

For a wave, $y=A\sin \frac{2\mathrm{\pi }}{\lambda }\left(\vartheta t-x\right)$, time-average of kinetic energy is given by:

The kinetic energy of pulse (in $mJ$) travelling in a taut string is $x.$ Given $T=10 \mathrm{N} \& \mu =0.1 \mathrm{kg}/\mathrm{m}.$ Find the value of $20 x.$

The clocktower ("ghantaghar") of Dehradun is famous for the sound of its bell, which can be heard, albeit faintly, upto the outskirts of the city $8 \mathrm{km}$ away. Let the intensity of this faint sound be $30 \mathrm{dB}.$ The clock is situated $80 \mathrm{m}$ high. The intensity at the base of the tower is:-

Two parallel boundaries separate three media as shown in figure. Planar wave of intensity I from continuous incoherent source is incident normally on $1\mathrm{st}$ boundary. Wave travels with speed $v,\frac{v}{2}$ and $\frac{v}{4}$ respectively in the media. Consider reflection and transmission of waves at each interface. Average energy density in steady state in medium $2$ (middle one) is $\frac{x}{3}\times {10}^{-7}\frac{\mathrm{J}}{{\mathrm{m}}^3}$. Value of $x$ is (consider $\frac{A_r}{A_i}=\left|\frac{V_t-V_i}{V_t+V_i}\right|$ where $A_r$ and $A_i$ are amplitudes of incident and reflected waves $V_t$ and $V_i$ are wave speed in media where transmitted and incident waves are present respectively)

(Take, $I={10}^{-5}\frac{\mathrm{W}}{{\mathrm{m}}^2};V=300 \mathrm{m}/\mathrm{s}$)

The ratio of intensities of two waves are given by $16:4$, then the ratio of amplitudes of the two waves is

A uniform string (length $L$,linear mass density $\mu$ and tension $F$ ) is vibrating with amplitude $A_n$ and frequency $f_n$ in its $n^{th}$ mode. The total energy of oscillation $E$ is given by :

At a certain instant, a stationary transverse wave produced in a string oscillating in fundamental mode fixed at both the ends is found to have maximum kinetic energy. The Amplitude at the antinode is $A$. The appearance of string at that instant is

A sound has an intensity of $2\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2}$. Its intensity level (in decibel) is: $\left({\log }_{10}2=0.3\right)$:

The intensity of light pulse travelling in an optical fiber decreases according to the relation $\mathrm{I}={\mathrm{I}}_0{\mathrm{e}}^{-\alpha x}$. The intensity of light is reduced to $20\%$ of its initial value after a distance $x$ equal to

A sensor is exposed for time $t$ to a lamp of power $P$ placed at a distance $l$. The sensor has a circular opening that is $4d$ in diameter. Assuming all energy of the lamp is given off as light, the number of photons entering the sensor if the wavelength of light is $\lambda$ is :- $\left(l>>d\right)$

Intensity due to point light source:-

$A$ is singing a note and at the same time $B$ is also singing a note with $1/8\mathrm{th}$ the frequency of $A.$ The energies of the two sounds are equal. The displacement amplitude of the note of $B$ is:

A longitudinal standing wave, $\text{y}=\text{a cos kx cos}\text{ω}\text{t}$  is maintained in a homogeneous medium of density $\text{ρ}$. Here $\text{ω}$ is the angular speed and k, the wave number and a is the amplitude of the standing wave. This standing wave exists all over a given region of space.

If a graph E (= E_P + E_K) versus t, (i.e.,) total space energy density versus time were drawn at the instants of time t = 0 and $\text{t}=\frac{\text{T}}{4}$, between two successive nodes separated by distance  $\frac{\text{λ}}{2}$  which of the following graphs correctly shows the total energy (E) distribution at the two instants.

A longitudinal standing wave, $\text{y}=\text{a cos kx cos}\text{ω}\text{t}$  is maintained in a homogeneous medium of density $\text{ρ}$. Here $\text{ω}$ is the angular speed and k, the wave number and a is the amplitude of the standing wave. This standing wave exists all over a given region of space.

The space density of the kinetic energy K.E = E_K (x, t) at the point (x, t) is given by

For next three question please follow the same

A longitudinal standing wave, $\text{y}=\text{a cos kx cos}\text{ω}\text{t}$  is maintained in a homogeneous medium of density $\text{ρ}$. Here $\text{ω}$ is the angular speed and k, the wave number and a is the amplitude of the standing wave. This standing wave exists all over a given region of space.

The space density of the potential energy P.E.= E_P (x, t) at a point (x, t) in the space is

In order to have half the velocity in the second case than in the first case, the potential applied should be

A point source emits sound in all directions in a non-absorbing medium. Two points P and Q are at distances of $2 \mathrm{m}$ and $3 \mathrm{m}$ respectively from the source. What will be the ratio of the intensities of that sound waves at point P and Q ?

Two waves represented by the following equations are travelling in the same medium

${\mathrm{y}}_1=5\sin 2\mathrm{\pi }\left(75\mathrm{t}-0.25\mathrm{x}\right)$

${\mathrm{y}}_2=10\sin 2\mathrm{\pi }\left(150\mathrm{t}-0.50\mathrm{x}\right)$

The intensity ratio $\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}$ of the two waves is

If A is the amplitude of the wave coming from a line source at a distance r, then

With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are