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Questions Related to physics

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

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) 

  1. 1.5

  2. 3

  3. 6

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The equation is y = 4 sin(4 * pi * t - pi * x / 16). Comparing to y = A sin(omega * t - k * x), omega = 4 * pi and k = pi / 16. Wave speed v = omega / k = 4 * pi / (pi / 16) = 64 cm/s. Since the signs of omega * t and k * x are opposite, the wave travels in the +x direction.

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

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 

  1. $c\, t/\pi$
  2. $c\, t/2\pi$
  3. $\pi/2k$
  4. $\pi/k$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The superposition of two waves traveling in opposite directions forms a standing wave. The distance between adjacent nodes is lambda / 2. Since k = 2 * pi / lambda, lambda / 2 = pi / k.

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

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 :

  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. $y=10\sin \left(\dfrac{x}{5}-8t+16\right)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave speed v = 40 cm/s. At t = 2 s, y = 10 cos(x / 5). The general form is y = 10 cos(x / 5 - omega * t + phi). Since v = omega / k, omega = v * k = 40 * (1 / 5) = 8 rad/s. At t = 2, y = 10 cos(x / 5 - 16 + phi) = 10 cos(x / 5). Thus, phi = 16.

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

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 :

  1. $ae^{-\left(\dfrac{x-ct}{b}\right)}$
  2. $ae^{\dfrac{ct+x}{b}}$
  3. $ae^{x-ct}$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A wave pulse moving in the positive x-direction with speed c has the form f(x - ct). Substituting (x - ct) into the initial shape f(x) = a * e^(-x/b) gives a * e^(-(x - ct) / b).

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

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:-

  1. 64 Hz

  2. 256 Hz

  3. 512 Hz

  4. 1024 Hz
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The fundamental frequency of a stretched wire is inversely proportional to its length, f proportional to 1 / L, when tension and mass density remain constant. When the length is decreased from 1 m (100 cm) to 25 cm, the length is reduced by a factor of 4, so the fundamental frequency increases by a factor of 4. Thus, f2 = 256 * 4 = 1024 Hz.

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

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 :

  1. $y=a\cos \omega t$
  2. $y=2a\cos \omega t$
  3. $y=a\cos \omega$ $\left(t-\dfrac{x}{c}\right)$
  4. $y=a\cos \left(\omega t+\dfrac{\omega x}{c}\right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a wave traveling in the negative x-direction, the argument is (omega * t + k * x). Given k = omega / c, the equation is y = a * cos(omega * t + omega * x / c).

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

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 $t=0.05\  s$?

  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. $y(0.5m,0.05s)=99cm/s$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $y(0.5m,0.05s)=89cm/s$

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

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.

  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. $\displaystyle \,y\,(x,\,t)\,=\,(0.97\,m)\,sin\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $y=(0.07m)sin2\pi(\dfrac{x}{0.32m}+\dfrac{t}{0.04s})$