Tag: speed of a travelling wave

Questions Related to speed of a travelling wave

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

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

  1. $2cps$

  2. $4cps$

  3. $6cps$

  4. All of these

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Correct Option: D
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.

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

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

  1. 3 m/s

  2. 5 m/s

  3. 2 m/s

  4. 7 m/s

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Correct Option: C
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.

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?

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

  1. $25$ m

  2. $20$ m

  3. $15$ m

  4. $10$ m

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Correct Option: D
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

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

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

  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.

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Correct Option: C

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

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

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

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

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

  4. $4 a ^ { 2 } \cos ^ { 2 } \delta / 2$

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Correct Option: D
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.



A body of mass $'m'$ is tied to the string and performing vertical circular motion. The tension in the string when string makes an angle $60^{\circ}$ with vertical is

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

  1. $6mg$

  2. $3mg$

  3. $9mg/ 2$

  4. $5mg/ 2$

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Correct Option: C

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

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

  1. $5.4 \mathrm { N }$

  2. $0.054 \mathrm { N }$

  3. $54 \mathrm { N }$

  4. $0.0054 N$

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Correct Option: A
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$5.4\,N$

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?

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

  1. $32 m$

  2. $16 m$

  3. $8 m$

  4. $4 m$

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Correct Option: B

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:-

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

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

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Correct Option: B

String $B$ has twice the length, twice the diameter, twice the tension and twice the density of string $A$. The overtone of $B$ that will be in unison with fundamental frequency of $A$ is 

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

  1. $1st$

  2. $2nd$

  3. $3rd$

  4. $4th$

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Correct Option: B