Energy of Wave

Q.

The total average energy density of e.m waves whose electric field variation is given by$e=(50\frac{N}{C})\sin (\omega t-kx)$ will be nearly

1. ${10}^{-8}J/m^3$

2. ${10}^{-6}J/m^3$

3. ${10}^{-10}J/m^3$

4. ${10}^{-12}J/m^3$

Q. A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

1. $60\text{mJ/s}$
2. $49\text{mJ/s}$
3. $40\text{mJ/s}$
4. $70\text{mJ/s}$

Q.

A plane electromagnetic wave is incident on a material surface. The wave delivers momentum $P$ and energy $E$

1. $P=0,E\ne 0$

2. $P\ne 0,E=0$

3. $P\ne 0,E\ne 0$

4. $P=0,E=0$

Q. A sinusoidal wave on a string is described by the wave function
$y=0.3\sin (1.6x-100t)$
where $x$ and $y$ are in $\text{metre}$ and $t$ is in $\text{second}$. The mass per unit length of this string is $10\text{g/m}.$ Determine the power transmitted to the wave.

1. $260\text{J}$
2. $281\text{J}$
3. $360\text{J}$
4. $320\text{J}$

Q. The equation of wave is given by $Y=A\sin \omega (\frac{x}{v}-k)$ where $\omega$ is the angular velocity and v is the linear velocity. The dimensions of k is:

1. $\left[LT\right]$
2. $\left[T\right]$
3. $\left[T^{-1}\right]$
4. $\left[T^{-2}\right]$

Q. A taut string for which $\mu =15\times {10}^{-2}\text{kg/m}$ is under a tension of $240\text{N}$. How much power must be supplied to the string to generate sinusoidal waves at a frequency of $18.0\text{Hz}$ and an amplitude of $18\text{cm}$?

1. $1300\text{W}$
2. $1240\text{W}$
3. $1280\text{W}$
4. $1220\text{W}$

Q. A sinusoidal transverse wave travels on a string of length $4\text{m}$ and mass $4\text{g}$. The wave speed is $20\text{m/s}$ and the wavelength is $0.2\text{m}$. If the wave is to have an average power of $50\text{W}$, then

1. tension induced in the string is $0.4\text{N}$.
2. frequency of wave will be $100\text{Hz}$.
3. linear mass density of the given string must be ${10}^{-3}\text{kg/m}$.
4. amplitude of the wave will be $11.25\text{cm}$

Q. A wave travels on a light string. The equation of the wave is $y=A\sin (kx-\omega t+{30}^{\circ }$). It is reflected from a heavy string tied to the end of the light string at $x=0$. If $64\%$ of the incident energy is reflected, then the equation of the reflected wave is

1. $y=0.8A\sin (kx-\omega t+{30}^{\circ }+{180}^{\circ })$
2. $y=0.8A\sin (kx+\omega t+{30}^{\circ }+{180}^{\circ })$
3. $y=0.8A\sin (kx-\omega t+{30}^{\circ })$
4. $y=0.8A\sin (kx+\omega t+{30}^{\circ })$

Q. A harmonic wave propagates in a medium. Find the average energy density of the wave, if at any point, the energy density becomes equal to $W_0$ at an instant $t=t_0+T/6$, where $t_0$ is the instant when amplitude is maximum at this location and $T$ is the time period of oscillation.

1. $\frac{3}{2}{W}_0$
2. $2W_0$
3. $\frac{2W_0}{3}$
4. $\frac{W_0}{2}$

Q. Statement (A): In a small segment of string carrying a sinusoidal wave, the total energy is conserved.

Statement (B) : Every small part of the string performs SHM and in SHM, the total energy is conserved .

1. Both (A) and (B) are correct
2. None of these
3. (A) is correct only
4. (B) is correct only

Q. For a particle of mass m enclosed in a one - dimensional box of length L, the de - Broglie concept would lead to stationary waves, with nodes at the two ends, The energy value allowed for such a system will be?

Q. A string has linear mass density, $\mu =0.1{\text{kg m}}^{-1}$, Length $L=60\text{cm}$ is clamped at $A$ and $B$ and is kept under a tension of $T=160\text{N}$. [The tension providing arrangement has not been shown in the figure]. A small paper rider is placed on the string at point $R$ such that $BR=20\text{cm}$. The string is set into vibrations using a tuning fork of frequency $f$.

1. The speed of wave set up along string is $40{\text{ms}}^{-1}$
2. The speed of waves set up along string is $20{\text{ms}}^{-1}$
3. If $R$ is a node, then the frequency of tuning fork, ${}^{\prime }{f}^{\prime }$ may be $100\text{Hz}$.
4. If $R$ is a antinode, then the frequency of tuning fork, ${}^{\prime }{f}^{\prime }$ may be $50\text{Hz}$.

Q.

A transverse wave of amplitude 0.50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is $100m{s}^{-1}$, what average power is the source transmitting to the wire ?

Q. Which of the following phenomena is due to propagation of a wave?

1. Vibration of a window panel when a supersonic aircraft passes
2. Breaking of glasses by opera singers by singing
3. Transportation of particles of a medium when a wave passes
4. Both (a) and (c)

Q. In a plane electromagnetic wave the electric field varies with the time having an amplitude of $1.0V{m}^{-1}$. Find the average energy density of magnetic field and that of electric field.

Q. A $400\text{Hz}$ wave with amplitude $2\text{mm}$ travels on a long string of linear mass density $5\text{g/m}$ kept under a tension of $50\text{N}$. Find the average power and total energy associated with the wave in a $2\text{m}$ long portion of the string.

1. $1\text{W}$ , $6\text{J}$
2. $6.32\text{W}$ , $0.13\text{J}$
3. $6\text{W}$ , $1\text{J}$
4. None of the above

Q.

Which electromagnetic wave has the most energy?

Q. given B=B₀sin(kx-wt), what is the magnetic energy density associated with the em wave?
and what is the energy density associated with the wave?(is it 2 times the first answer)?

Q. In a plane electromagnetic wave, the amplitude of the magnetic field is $5.0\times {10}^{-6}T$. Find the amplitude of the electric field and the total average energy density of the wave.

Q. Travelling wave travels in medium '1' and enters into another medium '2' in which it's speed gets decreased to $25\%$. Then magnitude of ratio of amplitude of transmitted to reflected wave is

1. $\frac{1}{7}$
2. $\frac{2}{3}$
3. $\frac{5}{9}$
4. $\frac{6}{5}$

Q. Find the electric field amplitude in an electromagnetic wave radiated by a $100$ W bulb at a distance $3$m from it, assuming an efficiency of a bulb is $2.5$% and it behaves like a point source.

1. $29$
2. $2.9$
3. $4.07$
4. $40.7$

Q. Figure shows a full wave bridge rectifier circuit. The input a.c. is connected across

1. A and B
2. A and C
3. B and D
4. B and C

Q. A sinusoidal wave (transverse) is produced on a string with frequency $f$ and amplitude $A$. The ratio of velocity amplitude to acceleration amplitude is

1. $\frac{-1}{2\pi f}$
2. $\frac{1}{\pi f}$
3. $\frac{2\pi }{f}$
4. $\frac{\pi }{f}$

Q. A plane electromagnetic wave is incident on a material surface. The wave delivers momentum p and energy E.
(a) p = 0, E ≠ 0
(b) p ≠ 0, E = 0
(c) p ≠ 0, E ≠ 0
(d) p = 0, E = 0

Q. Assertion :The mechanical energy between consecutive node and antinode will remain conserved in standing wave. Reason: The mechanical energy does not flow between node and antinode in standing wave.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. When longitudinal wave propagates through a medium, then the physical quantities propagating in the direction of wave are

1. Energy
2. Energy and mass
3. Energy, momentum and mass
4. Energy and momentum

Q. A massless rod $PQ$ is hanging from two identical string $AP$ and $BQ$ of equal length. At point $O$ a mass of $m\text{kg}$ is hanging at length $\frac{L}{5}$ from end $P$. If standing wave is set in string $AP$ and $BQ$ and the fundamental frequency of $AP$ is equal to $n^{th}$ harmonic of $BQ$. Then the value of $n$ is

Q. Travelling wave has frequency $f$ and particle displacement amplitude $A$. The particle velocity amplitude and particle acceleration amplitude are respectively

1. $fA$ & $f^{2}A$
2. $2\pi fA$ and $4{\pi }^2{f}^{2}A$
3. $A$ & $A$
4. cannot be found

Q. A sinusoidal wave on a string is described by the wave function
$y=0.3\sin (1.6x-100t)$
where $x$ and $y$ are in $\text{metre}$ and $t$ is in $\text{second}$. The mass per unit length of this string is $10\text{g/m}.$ Determine the power transmitted to the wave.

1. $260\text{J}$
2. $360\text{J}$
3. $281\text{J}$
4. $320\text{J}$

Q. Statement (A): In a small segment of string carrying a sinusoidal wave, the total energy is conserved.

Statement (B) : Every small part of the string performs SHM and in SHM, the total energy is conserved .

1. Both (A) and (B) are correct
2. (A) is correct only
3. (B) is correct only
4. None of these