Tag: oscillation and waves

Questions Related to oscillation and waves

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?

energy in wave motion oscillation and waves waves physics

  1. 5 : 2

  2. 5 : 4

  3. 4 : 5

  4. 25 : 4

Show answer
Correct Option: D
Explanation:

Energy density of wave is given by
$u=2\pi^2n^2pA^2$
or $u \propto A^2$   (As n and p are constant)
$\therefore \dfrac{u _1}{u _2}=\dfrac{A _1^2}{A _2^2}=\dfrac{5^2}{2^2}$
So, $u _1:u _2=25:4$

A progressive wave on a string having linear mass density $\rho$ is represented by $y = A\sin \left (\dfrac {2\pi}{\lambda} x - \omega t\right )$ where $y$ is in $10\ mm$. Find the total kinetic energy (in $\mu l)$ passing through origin from $t = 0$ to $t = \dfrac {\pi}{2\omega}$.
[Take : $\rho = 3\times 10^{-2} kg/ m; A = 1mm; \omega = 100\ rad/ sec; \lambda = 16\ cm]$

energy in wave motion oscillation and waves waves physics

  1. $6$

  2. $7$

  3. $8$

  4. $9$

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Correct Option: D

A clamped string is oscillating in nth harmonic, then 

energy in wave motion oscillation and waves waves physics

  1. total energy of oscillations will be $n^{2}$ times that of fundamental frequency

  2. total energy of oscillations will be $(n-1)^{2}$ times that of fundamental frequency

  3. average kinetic energy of the string over a complete oscillations is half of the total energy of the string

  4. none of these

Show answer
Correct Option: A,C
Explanation:

For a sine wave, $y = A \sin(kx -  \Omega  t)$
Velocity equation for this wave is $V _y =  \Omega A \cos(kx - \Omega  t)$
Kinetic energy = $ d(KE) = 1/2(V _y^2 \times dm) = 1/2(V _y^2 \times  \mu  dx)$, $ \mu $ is the linear mass density.


=> $1/2( \mu  \times  \Omega ^2 \times A^2 \times cos^2(kx -  \Omega  t)) dx$
integrating at $t = 0,$ with limits as $0$ and $ \lambda $, we have

$K.E = 1/4( \mu \times \Omega^2 \times A^2 \times  \lambda $)
Potential energy, $dU = 1/2 (  \Omega  ^2 \times y^2 \times  \mu ) dx $

integrating at $t = 0$, with limits as $0$ and $ \lambda $, we have
$U = 1/4( \mu \times \Omega  ^2 \times A^2 \times  \lambda $)

Total energy $E = K.E + U
$
=> $E = 1/2( \mu  A^2  \lambda $)
Therefore, for the first and fundamental frequency, energy is 
$E _1 = (1/2( \mu  A^2  \lambda ))/n^2$
And clearly from the above derivation, we have, K.E is half the total energy.

To determine the position of a point like object precisely ______ light should be used.

energy in wave motion oscillation and waves waves physics

  1. polarized

  2. short wavelength

  3. long wavelength

  4. intense

Show answer
Correct Option: B
Explanation:
To determine the position of a point like object precisely light of short wavelength should be used.

$mx^{2} - bx + k = 0$. Find time after which to the energy will become half of initial maximum value in damped forced oscillation.

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. $t = \dfrac {m}{b} + \dfrac {1}{2} ln2$

  2. $t = \dfrac {m}{b} \times \dfrac {2}{3} ln2$

  3. $t = \dfrac {m}{b} - \dfrac {1}{2} ln2$

  4. $t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$

Show answer
Correct Option: D
Explanation:

$\dfrac {1}{\sqrt {2}} = e^{-bt/m}$
$ln \sqrt {2} = \dfrac {bt}{m}$
$t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$.

The periodic vibrations of a body of constant amplitude in the absence of any external force on it are called

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All

Show answer
Correct Option: B
Explanation:

Forced vibrations: External force is acting on the body. 
Free vibration: Constant amplitude and no external force.
Damped vibration: Amplitude is not constant, it keeps on decreasing due to environmental factors of the system like air resistance.  
Therefore, correct option is B. 

The tendency of one object to force another adjoining or interconnected object into vibration motion is referred to as a 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. forced vibration.

  2. damped vibration

  3. loudness

  4. pitch

Show answer
Correct Option: A
Explanation:

The tendency of one object to force another adjoining or interconnected object into vibrating motion is referred to as a forced oscillation.

If a force is continually or repeatedly applied to keep the oscillation going, it is called 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. forced oscillator.

  2. free oscillatior

  3. damped oscillatior

  4. none of the above

Show answer
Correct Option: A
Explanation:

When a periodically repetitive and oscillatory force acts on an object, then the object is forced to oscillate with the frequency of the periodic force. Such oscillation is known as forced oscillation. When an object is displaced from its mean position and allowed to vibrate along its mean position then the object vibrates with its own natural frequency. This is known as free vibration or oscillation. And an oscillation in which the amplitude goes on decreasing with time is known as damped oscillation.

When we push a child in a swing, the amplitude of the oscillation

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. decreases

  2. increases

  3. remains same

  4. none of the above

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Correct Option: B
Explanation:

By pushing a child on a swing a driving force is applied which forces the swing and the child in the forward direction. The gravitational force acts as a restoring force and pulls back the child to the original position. These two forces together set them into an oscillatory motion. By pushing the child the amplitude, that is the maximum displacement, increases.

The orbital motion of the earth, around the sun is 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. periodic but not oscillatory

  2. oscillatory but not periodic

  3. neither periodic not oscillatory

  4. both periodic and oscillatory

Show answer
Correct Option: A
Explanation:

The orbital motion of the earth around the sun is not an oscillatory motion as it is not a two and fro motion about a mean position. But it is a periodic motion.