Tag: speed and acceleration of travelling wave

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Questions Related to speed and acceleration of travelling wave

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

A $12m$ long vibrating string has the speed of wave $48 m/s$ to what frequency it will resonate?

  1. $2cps$

  2. $4cps$

  3. $6cps$

  4. All of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given, $S=48m/s,l=12m$

So, Equation of the fundamental frequency:

$v\dfrac{v}{2l}=\dfrac{48}{2\times12}=2cps$

The string will resonate at fundamental frequency as well as first overtone second overtone and so on.
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A travelling wave tube is given by
$y = \dfrac{0.8}{(3x^2 + 12 xt + 12t^2 + 4)}$, where x and y are in m and t is in s . The velocity of the wave

  1. 3 m/s

  2. 5 m/s

  3. 2 m/s

  4. 7 m/s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} y=\dfrac { { 0.8 } }{ { 3{ x^{ 2 } }+12xt+12{ t^{ 2 } }+4 } }  \ =\dfrac { { 0.8 } }{ { 3\left( { { x^{ 2 } }+4x+4{ t^{ 2 } } } \right) +4 } }  \ =\dfrac { { 0.8 } }{ { 3{ { \left( { x+2t } \right)  }^{ 2 } }+4 } }  \ =\dfrac { { 0.8 } }{ { 3\times 4{ { \left( { \dfrac { x }{ 2 } +t } \right)  }^{ 2 } }+4 } }  \ \therefore Velocity=2m/s \end{array}$

$\therefore $ Option $C$ is correct.

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

Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10$ m $s^{-1}$. If the minimum time interval between two instant when the string is flat is $0.5$s, the wavelength of the waves is?

  1. $25$ m

  2. $20$ m

  3. $15$ m

  4. $10$ m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given frequency $f$=$\dfrac { 1 }{ t } $ and velocity $\nu$=10 m/s

We know $\nu =\lambda f\ \lambda =\dfrac { \nu  }{ f } =\dfrac { 10 }{ \frac { 1 }{ 0.5 }  } =5\quad m\ $
Since both the waves are similar but moves in opposite direction its toatl wavelength of the wave will be 10 m

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

Mark out the correct statements with respect to wave speed and particle velocity for a transverse travelling mechanical wave on a string.

  1. The wave speed is same for the entire wave, while particle velocity is different for different points at a particular instant.

  2. Wave speed depends upon property of the medium but not on the wave properties.

  3. Wave speed depends upon both the properties of the medium and on the properties of wave.

  4. Particle velocity depends upon properties of the wave and not on medium properties.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave speed v = sqrt(T/mu) depends only on the properties of the medium (tension T and linear density mu). Particle velocity depends on the wave's amplitude and frequency, which are properties of the wave itself.

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

Two waves $Y _ { 1 } =  { a \sin \omega t }$  and  $Y _ { 2 } = \operatorname { asin } ( \omega t + \delta )$  are producing interference, then resultent intensity is:

  1. $a ^ { 2 } \cos ^ { 2 } \delta / 2$

  2. $2 a ^ { 2 } \cos ^ { 2 } \delta / 2$

  3. $3 a ^ { 2 } \cos ^ { 2 } \delta / 2$

  4. $4 a ^ { 2 } \cos ^ { 2 } \delta / 2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$Y _{1}+Y _{2}=a\sin\omega t+a\sin(\omega t+8)$
$Y=a\left[\sin\omega t+\sin(\omega t+8)\right]$
$Y=a\left[2\sin\left(\dfrac{\omega t+\omega t+8}{2}\right)\cos\left(\dfrac{8}{2}\right)\right]$
$Y=2a\sin\left(\omega t+\dfrac{8}{2}\right)\cos\left(\dfrac{8}{2}\right)$
$Y=\left[2a\cos \left(\dfrac{8}{2}\right)\right]\sin(\omega t+8/2)$
As Intensity $\alpha A^{2}$
Here $I \alpha \left[2a\cos\left(\dfrac{8}{2}\right)\right]^{2}$
$I\alpha 4a^{2}\cos^{2}\left(\dfrac{8}{2}\right)$
Option $D$ is correct.



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

A transverse wave propagating on the string can be described by the equation  $y = 2 \sin ( 10 x + 300 t ).$  where $x$  and  $y$  are in metres and  $t$  in second. If the vibrating string has linear density of  $0.6 \times 10 ^ { - 3 } \mathrm { g/cm }$  then the tension in the string is

  1. $5.4 \mathrm { N }$

  2. $0.054 \mathrm { N }$

  3. $54 \mathrm { N }$

  4. $0.0054 N$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

General equation of progressive wave:

$y = A \sin ( \omega t + k x )$

Here, $A$ is amplitude

$\omega$ is angular frequency

$k\,$is propagation constant

$t$  is time

$x$ is displacement

Given equation:

$y = 2 \sin ( 10 x + 300 t ).$

Linear charge density, $\mu =0.6\times {{10}^{-3}}\text{g/cm}\,\text{=}\,6\times \text{1}{{\text{0}}^{-3}}\,kg{{m}^{-1}}$
 

Compare with general equation:

Velocity of the wave in the string:

$v = \dfrac { \omega } { k }$$=\dfrac{300}{10}\text{=30}\,\text{m}{{\text{s}}^{-1}}$

Relation for velocity in terms of tension:

$T = \mu v ^ { 2 }$$=6\times {{10}^{-3}}\times {{(30)}^{2}}=5.4\,N$

Hence, tension in string is$5.4\,N$

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

A person observe two points on a string as a travelling wave passes them. The points are at $x _ { 1 } = 0$ and $x _ { 2 } = 1 m.$ The transverse motions of the two points are found to be as follows:
$y _ { 1 } = 0.2 \sin 3 \pi t$
$y _ { 2 } = 0.2 \sin ( 3 \pi t + \pi/8 )$
What is the maximum wavelength?

  1. $32 m$

  2. $16 m$

  3. $8 m$

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

The phase difference delta_phi = k * delta_x. Given y1 = 0.2 sin(3 * pi * t) and y2 = 0.2 sin(3 * pi * t + pi/8), the phase difference is pi/8 for a distance delta_x = 1 m. Thus, k = (pi/8) / 1 = pi/8. Since k = 2 * pi / lambda, we have pi/8 = 2 * pi / lambda, so lambda = 16 m.

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

A string of length $L$ is stretched along the $x-axis$ and is rigidly clamped at its two ends. It undergoes transverse vibration. If $n$ is an integer, which of the following relations may represent the shape of the string at any time:-

  1. $y = A \sin \left( \dfrac { n \pi x } { L } \right) \cos \omega t$

  2. $y = A \sin \left( \dfrac { n \pi x } { L } \right) \sin \omega t $

  3. $y = A \cos \left( \dfrac { n \pi x } { L } \right) \cos \omega t $

  4. $y = A \cos \left( \dfrac { \operatorname { n\pi } x } { L } \right) \sin \omega t$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a string fixed at both ends, the standing wave must satisfy boundary conditions y = 0 at x = 0 and x = L. The form y = A sin(n * pi * x / L) * sin(omega * t) satisfies these conditions.