Tag: wave velocity

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Questions Related to wave velocity

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

 A solid cylinder of mg 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to and hanging freely. Tension in the string required to produce angular acceleration of revolutions $s ^ { - 2 }$ is

  1. 78.5 N

  2. 157 N

  3. 25 N

  4. 50 N
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mass=m=50kg

Radius=0.5m
Angular acceleration$=\alpha=2 rev/s^{2}$
Torque$=T \times R = T \times 0.5= \cfrac{T}{2} Nm ------(i)$
We know, $T=1 \alpha------(ii)$
From (i) and (ii),
$\cfrac{T}{2}=1 \alpha = \left( \cfrac{MR^{2}}{2} \right) \times (2 \times 2 \pi) rad/s^{2}$
$\therefore 1$ solid cylinder$=\cfrac{MR^{2}}{2}$
$\cfrac { T }{ 2 } =\cfrac { 50\times { (0.5) }^{ 2 } }{ 2 } \times 4\pi =50\pi =157N$

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

The vibration of a string of length 60 cm fixed at both ends are represented by $ y=4sin (\frac { \pi x}{15}) cos (96 \pi t) $ where x and y are in cm and t in second. the particle velocity at x=7.5 cm and t=0.25 s is

  1. Zero
  2. $ 10 cm s^{-1} $
  3. $ 100 cm s^{-1} $
  4. $ (4 \times 96) cm s^{-1} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The particle velocity is given by the partial derivative of y with respect to t. Since the wave is a standing wave, the velocity is v = dy/dt = -4 * 96 * pi * sin(pi*x/15) * sin(96 * pi * t). At t = 0.25 s, sin(96 * pi * 0.25) = sin(24 * pi) = 0, so the velocity is zero.

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

A $100$ Hz sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of $3.5 \times 10^{-3}$ kg/m and a tension of $35$ N. At time t = 0, the point x = 0 has zero displacements and the slope of the string is $\pi/20$. Then select the wrong alternative

  1. Velocity of wave is $100$ m/s
  2. Angular frequency is $(200 \pi)$ rad /s
  3. Amplitude of wave is $0.025$ m
  4. Propagation constant is $(4 \pi)$ $m^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A uniform string fixed at both ends is vibrating in 3rd harmonic and equation $y = 4 ( \mathrm { cm } )$ $\sin \left[ \left( 0.8 \mathrm { cm } ^ { - 1 } \right) \times \right] \cos \left[ \left( 400 \pi \mathrm { s } ^ { - 1 } \right) t \right]$The length of the vibrating string is

  1. $6.75 \mathrm { m }$
  2. $12.45 \mathrm { m }$
  3. $11.8 \mathrm { m }$
  4. $18.7 \mathrm { m }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$ y=4\sin  \left( { 0.8x } \right) \cos  \left( { 400\pi t } \right)  \ w=400\pi =2\pi f \ f=200\, Hz \ v=\dfrac { w }{ k } =\dfrac { { 400\pi \times 100 } }{ { 0.8 } } m/s \ 3\cdot \dfrac { v }{ { 2l } } =f \ \Rightarrow 200=\dfrac { { 3\times 400\pi \times 100 } }{ { 2\times l\times 0.8 } }  \ \Rightarrow l=\dfrac { { 3\times 400\pi  } }{ { 4\times 0.8 } }  \ =\dfrac { { 300\pi  } }{ { 0.8 } } \, cm \ =11.8\, m$

Hence,
option $(C)$ is correct answer.

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

The wave function for the wave pulse is $ Y (X,t) = \frac {0.1a^3}{a^2 +(X-Vt)^2}  with a = 4 cm. At X = 0 $ The displacement y (x,t) is observed to decreases from its maximum value to half of that value in time $ t = 2 \times 10^{-3} s $ choose the correct statement 

  1. The wave pulse is moving is negative X direction with speed 10 m/s

  2. The wave pulse is moving is positive X direction with speed 10 m/s

  3. The wave pulse is moving is negative X direction with speed 20 m/s

  4. The wave pulse is moving is positive X direction with speed 20 m/s
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A string is properly tuned:

  1. When the beat frequency vanishes.

  2. When the beat frequency is maximum.

  3. When the beat frequency is minimum.

  4. When the beat frequency is between maximum and minimum.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Beats are produced when two sound waves of slightly different frequencies interfere. When the two frequencies are identical, the beat frequency becomes zero, meaning the beat frequency vanishes, indicating that the string is properly tuned.

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

A heavy flexible rope hangs vertically. The speed of a transverse wave at a height $h$ from the free end is

  1. $\sqrt { g h }$
  2. $\sqrt { g / h }$
  3. $\sqrt { 2 g h }$
  4. $\sqrt { h / g }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The tension at a distance h from the free end of a hanging rope is T = mu * g * h, where mu is the linear mass density. The wave speed is v = sqrt(T/mu) = sqrt(mu * g * h / mu) = sqrt(g * h).

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

A tension in wire is 40N and 10 m of wire has a mass of 0.01 kg . The speed of transverse waves in m/s in the wire is :

  1. 200

  2. 80

  3. 300

  4. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know, Speed of transverse wave $(v) = \sqrt{\dfrac{T}{\mu}}$


where, T = Tension = 40N and  $\mu = $ mass per unit length = $\dfrac{0.01}{10} = 10^{-3}\; kg/m$ 

$\Rightarrow v = \sqrt{\dfrac{40}{10^{-3}}} = 200 m/s$

Therefore, A is correct option.

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

A string of mass $2.5\ kg$ is under a tension of $200\ N$. The length of the stretched string is $20.0\ m$. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in

  1. One second
  2. $0.5$ second
  3. $2\ seconds$

  4. Data given is insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Linear mass density mu = mass / length = 2.5 kg / 20 m = 0.125 kg/m. Wave speed v = sqrt(T / mu) = sqrt(200 / 0.125) = sqrt(1600) = 40 m/s. Time taken t = distance / speed = 20 m / 40 m/s = 0.5 s.