Tag: physics

Questions Related to physics

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

A long string having a cross-sectional area $0.80 mm^2$ mm2and density, $12.5 g/cc$ is subjected to a tension of $64 N$ along the positive x-axis. One end of this string is attached to a vibrator at $x = 0$ moving in transverse direction at a frequency of $20 Hz$. At $t = 0$, the source is at a maximum displacement $y = 1.0 cm.$ What is the velocity of this particle at the instant when $x=50\ cm$  and time $t=0.05\  s$?

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

  1. $y(0.5m,0.05s)=98cm/s$

  2. $y(0.5m,0.05s)=59cm/s$

  3. $y(0.5m,0.05s)=89cm/s$

  4. $y(0.5m,0.05s)=99cm/s$

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Correct Option: C
Explanation:
Mass per unit length of the string=$\mu=\rho A=0.8\times 10^{-6}\times 12.5\times 10^{3}=0.01kg/m$
Thus speed of the wave=$\sqrt{\dfrac{T}{\mu}}=\sqrt{\dfrac{64}{0.01}}=80m/s$

Amplitude of the wave=A=1cm
$\omega=2\pi\nu=40\pi s^{-1}$
$v=\dfrac{\omega}{k}$
$\implies k=\dfrac{40\pi}{80}=\dfrac{\pi}{2} m^{-1}$
Thus the wave equation is $y=Acos(\omega t-kx)$
$=(1cm)cos[(40\pi s^{-1})t-(\dfrac{\pi}{2}m^{-1})x]$
Hence velocity of a particle=$-\dfrac{dy}{dt}=-\omega A sin(\omega t-kx)$
Thus $y(0.5m,0.05s)=89cm/s$

Transverse waves on a string have wave speed $8.00$ m/s, amplitude $0.0700\  m$ and wavelength $0.32\  m$. The waves travel in the negative x-direction and $t = 0$ the $x = 0$ end of the string has its maximum upward displacement. Write a wave function describing the wave.

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

  1. $\displaystyle \,y\,(x,\,t)\,=\,(0.07\,m)\,sin\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$

  2. $\displaystyle \,y\,(x,\,t)\,=\,(77\,m)\,cos\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$

  3. $\displaystyle \,y\,(x,\,t)\,=\,(0.7\,m)\,sin\,4\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$

  4. $\displaystyle \,y\,(x,\,t)\,=\,(0.97\,m)\,sin\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$

Show answer
Correct Option: A
Explanation:

A left travelling transverse wave given by $y=Asin(kx+\omega t)$

where wave number,$k=\dfrac{2\pi}{\lambda}=\dfrac{2\pi}{0.32}rad/m$
Speed of wave=$\lambda\nu=8m/s$
$\implies \nu=\dfrac{8}{0.32}Hz=25Hz$
$\implies \omega=2\pi\nu=\dfrac{2\pi}{0.04s}$
Thus $y=(0.07m)sin2\pi(\dfrac{x}{0.32m}+\dfrac{t}{0.04s})$