Tag: wave motion

Questions Related to wave motion

An elastic string carrying a baby of mass 'm' extends by 'e' . The body rotates in a vertical circle with critical velocity. The externsion in the string at the lowest position is 

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $2e$

  2. $4e$

  3. $6e$

  4. $8e$

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Correct Option: C

The equation of a progressive wave for a wire is: 
$Y=4\sin{\left[\cfrac{\pi}{2}\left(8t-\cfrac{x}{8}\right)\right]}$. If $x$ and $y$ are measured in cm then velocity of wave is :

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $64 cm/s$ along $-x$ direction

  2. $32 cm/s$ along $-x$ direction

  3. $32 cm/s$ along $+x$ direction

  4. $64 cm/s$ along $+x$ direction

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Correct Option: D
Explanation:

$\begin{array}{l} w=4\pi  \ K=\dfrac { \pi  }{ { 16 } }  \ v=\dfrac { w }{ K } =64\, m/s\, along\, \, +x-axis \ Hence, \ option\, \, D\, \, is\, correct\, \, answer. \end{array}$

An open tube is in resonance with string (frequency of vibration of tube in $n _{0}$. If tube is dipped on water is that 75% of length of tube is inside water, then the ratio of the frequency of tube to string now will be 

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. 1

  2. 2

  3. $\dfrac{2}{3}$

  4. $\dfrac{3}{2}$

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Correct Option: B
Explanation:
For open tube no $ = \dfrac{V}{2l} $
For closed tube length available for resonance
$ l^{1} ,l\times \dfrac{25}{100} = \frac{l}{4} $
fundamental frequency of water filled tube 
$ n _{1}\dfrac{V}{4l^{1}} = \frac{V}{4(l/4)} $ $(\because l^{1}= l/4) $
$ \therefore \dfrac{V}{l} = 2n _{0} = 1 $
$ = \dfrac{n}{n _{0}} = 2 $

The equation of a standing wave in a string fixed at both ends is given as $ y =  A \quad sin \quad  kx \quad cos \quad \omega t $
The amplitude and frequency of a particle vibrating at the mid of an antiode and a node are respectively

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $A,\dfrac{\omega }{{2\pi }}$

  2. $\dfrac{A}{{\sqrt 2 }},\dfrac{\omega }{{2\pi }}$

  3. $A,\dfrac{\omega }{{\pi }}$

  4. $\sqrt 2 A,\dfrac{\omega }{{2\pi }}$

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Correct Option: A

A wire of length l , area of cross section A  and young's modules of elasticity  y is  suspended from the roof of a building. A  block of mass m is attached at lower end of the wire. if the block is displaced from its mean position and then released the block starts  oscillating. Time period of these oscillation will be

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $2\pi \sqrt { \frac { Al }{ mY } } $

  2. $2\pi \sqrt { \frac { AY }{ ml } } $

  3. $2\pi \sqrt { \frac { ml }{ YA } } $

  4. $2\pi \sqrt { \frac { m }{ YAl } } $

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Correct Option: B

Which of the following equations represents a transverse wave travelling along -y axis?

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $x = A\sin\ (\omega t\ -\ ky)$

  2. $x= A\ sin\ (\omega t\ +\ ky)$

  3. ${ y } _{ 0 }\ =A\sin\ (\omega t - kX   )$

  4. ${ y } _{ 0 } = A\ sin (\omega t + kX )$

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Correct Option: B
Explanation:

$\begin{array}{l} For\, \, negative\, \, y-axis \ sign\, \, of\, \, \omega t\, \, & \, \, ky\, \, should\, \, be\, \, same\,  \ x=A\sin  \left( { \omega t+ky } \right)  \ Hence, \ option\, \, B\, \, is\, correct\, \, naswer. \end{array}$

The displacement from the position of equilibrium of a point $4\ cm$ from a source of sinusoidal oscillations is half the amplitude at the moment $t=\dfrac{T}{6} (T$ is the time period$)$. Assume that the source was at mean position at $t=0$. The wavelength of the running wave is 

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $0.96\ m$

  2. $0.48\ m$

  3. $0.24\ m$

  4. $0.12\ m$

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Correct Option: B
Explanation:

Going by the data given to us, this wave is sinusoidal in nature and the wave equation takes the form of
$y = A\sin( \omega t - kx),$ as it is given that at $t = 0,$  the source is at mean position.
Here$,\ x = 4\ cm = 0.04\ m$
$y = A/2$
Amplitude $= A$
$t = \dfrac{T}{6}$
We know that $ \omega  = 2 \dfrac{ \pi }{T}$
$\Rightarrow \dfrac{A}{2} = A\sin((2  \pi  / T)(T/6) - 0.04k)$
$\sin((2 \pi  / T)(T/6) - 0.04k) = 1/2$
$\Rightarrow ((2  \pi / T)(T/6) - 0.04k) =  \pi / 6$
$k =  \pi  / 0.24$
wavelength $ \lambda = 2\pi  / k = 0.48\ m$

A string of length 1 m fixed at one end and on the other end a block of mass M=4 kg is suspended.The string is set into vibrations and represented by equation, Y=$6\sin \left( {\dfrac{{\pi x}}{{10}}} \right)\;\cos \;100\;\pi t,$  where x and y are in cm an in seconds.
Find the number of loops formed in the string.

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. 3

  2. 4

  3. 5

  4. 6

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Correct Option: A

A travelling wave is given by $y=\frac { 0.8 }{ 3{ x }^{ 2 }+12xt+12{ t }^{ 2 }+1 } $ where x and y are is m and t is in sec, then velocity and amplitude wave will be

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. 2m/s, 0.2m

  2. 4m/s, 0.2m

  3. 2m/s, 0.4m

  4. none

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Correct Option: D

A travelling wave on a light on a tight string is described by the equation $y=A\sin (kx-\omega t)$. if tension in the string is $F$ then total energy stored in the string having from $x=0$ to $x=2\pi/k$ is 

physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

  1. $\pi FA^{2}$

  2. $\pi kFA^{2}$

  3. $\pi k^{2}FA$

  4. $none\ of\ these$

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Correct Option: A