Tag: wave motion

Questions Related to wave motion

Which of the following statements is correct?

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

  1. Longitudinal waves consist of crests and troughs

  2. In case of transverse waves, the particles of the medium vibrate at right angles to the direction of wave

  3. Transverse waves are produced when a tuning fork is struck in air

  4. Longitudinal waves are produced when a stone is dropped on the surface of water in a pond

Show answer
Correct Option: C
Explanation:

Answer is C.

A transverse wave is a wave in which the medium vibrates at right angles to the direction that the wave travels. An example of a transverse wave is a wave in a rope held with a hand on one end and tied to a pole on another end.
In this wave, energy is provided by a persons hand moving one end of the rope up and down. The direction of the wave is down the length of the rope away from the persons hand. The rope itself moves up and down as the wave passes through it.
The characteristic described in statement c is a property of all transverse waves, but not necessarily of all mechanical waves. A mechanical wave can also be longitudinal.
Hence, option C is correct and rest of the statements are incorrect.

Common balance reading on earth of an object is 'X' and the spring balance reading is 'Y'. The set up is transferred to moon. What reading does the common balance and spring balance give?

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

  1. $\dfrac{X}{6}, Y$

  2. $X, \dfrac{Y}{2}$

  3. $X, \dfrac{Y}{6}$

  4. $X, \dfrac{Y}{3}$

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Correct Option: C

Two vibrating strings of the same material but length $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the string vibrate in their fundamental modes, the one of length $L$ with frequency ${v} _{1}$ and other with frequency ${v} _{2}$. The ratio ${v} _{1}/{v} _{2}$ is given by

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

  1. $2$

  2. $4$

  3. $8$

  4. $1$

Show answer
Correct Option: D
Explanation:
For vibrating string 
frequency $\alpha \dfrac{1}{lenght} \sqrt{\dfrac{Tension}{mass\ per\ unit\ lenght}}$ ---- $(1)$
Since area of first wire is $\dfrac{\pi (2)^{2}}{\pi 1^{2}} = 4$ times pf second wire
its mass per unit length is also $4$ times 
i.e. $\mu _{1}= 4 \mu$ $\mu _{2}= \mu$
$v _{1} = \dfrac{1}{L} \sqrt{\dfrac{T}{4\mu}}= \dfrac{1}{\mu} \sqrt{\dfrac{T}{\mu}}$
$v _{2}= \dfrac{1}{2} \sqrt{\dfrac{T}{\mu}}$
$\dfrac{v _{1}}{v _{2}}= \dfrac{1}{2L} \sqrt{\dfrac{T}{\mu}} \times  \dfrac{2l}{1} \sqrt{\dfrac{\mu}{T}}$
$=1$

A sonometre wire resonates with a given tuning forck forming standing waves with five antinodes between the two bridges when a mass of $9kg$is suspended from the wire. When this mass is replaced by mass $M$, the wire resonates with the same positions of the bridges. Then find the value of square roof of $M$.

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

  1. $5$

  2. $10$

  3. $25$

  4. $None$

Show answer
Correct Option: C
Explanation:

The frequency of vibration of a string 

$n=\dfrac{p}{2l}\sqrt{\dfrac{T}{m}}$
Also number of loops = Number of antinodes.
Hence with 5 antinodes and hanging mass of 9 kg. we have p=5 and T=9g
So,
$n _1=\dfrac{5}{2l}\sqrt{\dfrac{9g}{m}}$
With 3 antinodes and hanging mass M we have p=3 and T=Mg so,
$n _2=\dfrac{3}{2l}\sqrt{\dfrac{Mg}{m}}$
$\because n _1=n _2$
$\dfrac{5}{2l}\sqrt{\dfrac{9g}{m}}=\dfrac{3}{2l}\sqrt{\dfrac{Mg}{m}}$
Squaring both side we get
$25\times9=9\times M$
$M=25\ kg$

A travelling wave on a string is given by $y=A\ \sin [\alpha x+\beta t+\dfrac {\pi}{6}]$. The displacment oscillation of a point $\alpha=0.56\ /cm,\beta=12/sec,A=7.5\ cm,x=1\ cm$ and $t=1s$ is

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

  1. $4.6\ cm,46.5\ cms^{1}$

  2. $3.75\ cm,77.94\ cms^{1}$

  3. $1.76\ cm,7.5\ cms^{1}$

  4. $7.5\ cm,75\ cms^{1}$

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Correct Option: A

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

Show answer
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

Show answer
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

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

Show answer
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.