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 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:-

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 :- $\left(l>>d\right)$

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

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

A simple harmonic oscillator of frequency $f$ is attached to the end of a cord that has a linear mass density $\mathrm{\mu }$ and is under a tension $T$. The power that must be provided to the cord by the oscillator to generate a sinusoidal wave of amplitude $A$ angular frequency $\mathrm{\omega }$ and velocity $v$ is

The ends of a stretched wire of length L are fixed at $x=0$ and $x=L$. In one experiment the displacement of the wire is ${\mathrm{y}}_1=\mathrm{A}\sin \left(\frac{\mathrm{\pi }\mathrm{x}}{\mathrm{L}}\right)\sin \mathrm{\omega }\mathrm{t}$ and energy is ${\mathrm{E}}_1$ and in other experiment its displacement is ${\mathrm{y}}_2=\mathrm{A}\sin \left(\frac{2\mathrm{\pi }\mathrm{x}}{\mathrm{L}}\right)\sin 2\mathrm{\omega }\mathrm{t}$ and energy is ${\mathrm{E}}_2$ .

Then:

Displacement-time graphs for two waves, wave-1 and wave-2 are shown here. Ratio of intensity of wave-1 to that of wave-2 is

A point source is emitting sound in all directions. The ratio of distance of two points from the point source where the difference in loudness levels is $3 \mathrm{dB}$ $({\mathrm{l}\mathrm{o}\mathrm{g}}_{10}2\mathrm{ }=\mathrm{ }0.3)$

Displacement-time graphs for two waves, wave-1 and wave-2 are shown here. Ratio of intensity of wave-1 to that of wave-2 is

A point source emits sound equally in all direction in a non-absorbing medium. Two points P and Q are at distance of 2 and 3 m respectively from the source. The ratio of the intensities of the wave at P and Q is.

The amplitude of two waves are in ratio $5:2$. If all other conditions for the two waves are same, then what is the ratio of their energy densities?

The equation of a cylindrical progressive wave is

A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $4 \mathrm{m}$ and $9 \mathrm{m}$, respectively from the source. The ratio of amplitudes of the waves at $P$ and $Q$ is 

In a grease spot photometer, light from a lamp with dirty chimney is exactly balanced by a point source distance 10 cm from the grease spot. On clearing the dirty chimney, the point source is moved 2 cm to obtain a balance again. Then the percentage of light absorbed by the dirty chimney is nearly

SI unit of intensity of wave is

A sinusoidal wave with amplitude y is travelling with speed $v$ on a string with linear density $\rho$. The angular frequency of the wave is $\omega$ . The following conclusions are drawn. Mark the one which is correct. (in particular option if we are changing one quantity assume others are kept constant)

A sinusoidal wave with amplitude y is travelling with speed $v$ on a string with linear density $\rho$. The angular frequency of the wave is $\omega$. The following conclusions are drawn. Mark the one which is correct. (in particular option, if we are changing one quantity, assume others are kept constant)