Tag: wave motion

Questions Related to wave motion

A wave represented by a given equation $y (x,t) = a \sin (\omega t - kx)$superimposes on another wave giving a stationary wave having antinode at $x = 0 $ then the equation of the another wave is 

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

  1. $y = - a \sin (\omega t - kx)$

  2. $y = a \sin (\omega t + kx)$

  3. $y = - a \sin (\omega t + kx)$

  4. $y = - a \cos (\omega t + kx)$

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Correct Option: B
Explanation:

$\begin{array}{l} a\sin  \left( { wt-kx } \right) +{ y _{ 1 } }=2a\sin  \cot  \cos  kx \ \Rightarrow y=a\sin  \left( { wt+kx } \right)  \ Ans.\, \, (B) \end{array}$

A travelling wave passes  point of observation. At this point, the time interval between successive crests is $0.2\, s$ and 

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

  1. The wavelength is $5\, m$

  2. The frequency is $5\, Hz$

  3. The velocity of propagation is $5\, m/s$

  4. The wavelength is $0.2\, m$

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Correct Option: B
Explanation:

$\begin{array}{l} Accorrding\, \, to\, \, question....................... \ Here, \ Difference\, between\, two\, successive\, crest\, is\, 2p. \ passes\, difference\, (\Delta \varphi )=\frac { { 2\pi  } }{ T }  \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, T=time\, { { int } }erval(\Delta t) \ \therefore \, \, \, n=2\pi =\frac { { 2\pi  } }{ T } \times 0.2 \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Rightarrow \frac { 1 }{ T } =5{ \sec ^{ -1 }  } \ \Rightarrow n=5Hz \ So\, the\, correct\, option\, is\, B. \end{array}$

The equation of standing wave in a stretched string is given by by y = 5sin($\frac{{\pi}{x}} {3}$) cos $(40{\pi}t)$, where x and y are in cm and t in second. The separation between two consecutive nodes is (in cm) 

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

  1. 1.5

  2. 3

  3. 6

  4. 4

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Correct Option: B
Explanation:

$\begin{array}{l} y=5\sin  \left( { \frac { { \pi x } }{ 3 }  } \right) .\cos  \left( { 4\pi t } \right)  \ Here\, in\, above\, equation\, \, k=\frac { \pi  }{ 3 }  \ \frac { { 2\pi  } }{ \lambda  } =\frac { \pi  }{ 3 }  \ \lambda =6cm \ Hence,\, dis\tan  ce\, between\, 2\, nodes\, is\, \frac { \lambda  }{ 2 } =3cm \end{array}$

Hence, the option $B$ is the correct answer.

The equation of a wave travelling on a string is $y=4 sin \left[ \dfrac { \pi  }{ 2 } \left( 8t-\dfrac { x }{ 8 }  \right)  \right] $, where $x,y$ are in cm and $t$ is in second. The velocity of the wave is

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

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

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

  3. $32 cm/s$ in $+x-$ direction

  4. $64 cm/s$ in $+x-$ direction

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Correct Option: D

Two travelling waves $y _1=A sin[k(x-ct)]$ and $y _2\, sin[k(x+ct)]$ are superimposed on string. The distance between adjacent nodes is 

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

  1. $c\, t/\pi$

  2. $c\, t/2\pi$

  3. $\pi/2k$

  4. $\pi/k$

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Correct Option: D

A wave propagates on a string in positive $x-$ direction with a speed of $40\ cm/s$. The shape of string at $t=2\ s$ is $y=10\cos \,\dfrac{x}{5}$, where $x$ and $y$ are in centimetre. The wave equation is :

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

  1. $y=10\cos \left(\dfrac{x}{5}-8t\right)$

  2. $y=10\sin \left(\dfrac{x}{5}-8t\right)$

  3. $y=10\cos \left(\dfrac{x}{5}-8t+16\right)$

  4. $y=10\sin \left(\dfrac{x}{5}-8t+16\right)$

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Correct Option: C

A wave pulse is propagating with speed $c$ towards positive $x-$axis. The shape of pulse at $t=0$, is $y=ae^{-x/b}$ where $a$ and $b$ are constant. The equation of wave is :

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

  1. $ae^{-\left(\dfrac{x-ct}{b}\right)}$

  2. $ae^{\dfrac{ct+x}{b}}$

  3. $ae^{x-ct}$

  4. $none\ of\ these$

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Correct Option: A

1 meter long stretched wire of a sonometer vibrates with its fundamental frequency of 256 Hz. If the length of the wire is decreased to 25 cm and the tension remains the same, then the fundamental frequency of vibration will be:-

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

  1. 64 Hz

  2. 256 Hz

  3. 512 Hz

  4. 1024 Hz

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Correct Option: A

In a stretched string, 

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

  1. Only transverse waves can exist

  2. Only longitudinal waves can exist

  3. Both transverse and longitudinal waves can exist

  4. None of these

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Correct Option: A

A travelling wave is propagating along negative $x-$axis through a stretched string. The displacement of a particle of the string at $x=0$ is $y=a\cos \omega t$. The speed of wave is $c$. The wave equation is :

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

  1. $y=a\cos \omega t$

  2. $y=2a\cos \omega t$

  3. $y=a\cos \omega$ $\left(t-\dfrac{x}{c}\right)$

  4. $y=a\cos \left(\omega t+\dfrac{\omega x}{c}\right)$

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Correct Option: D