Tag: physics

Quizzes (598) Questions (13441)

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

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. <span>$y(0.5m,0.05s)=98cm/s$</span>

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

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

  4. <span>$y(0.5m,0.05s)=99cm/s$</span>
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. <span>$\displaystyle \,y\,(x,\,t)\,=\,(0.07\,m)\,sin\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$</span>

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

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

  4. <span>$\displaystyle \,y\,(x,\,t)\,=\,(0.97\,m)\,sin\,2\,\pi\,\left ( \frac{x}{0.32\,m}\,+\,\frac{t}{0.04\,s} \right )$</span>
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 $y=(0.07m)sin2\pi(\dfrac{x}{0.32m}+\dfrac{t}{0.04s})$