Tag: speed of a travelling wave

Questions Related to speed of a travelling wave

A particle starting from mean position having equation $y=A\sin { \pi t } $ .Find velocity of particle at t=1/3 sec.

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

  1. $\dfrac { A\pi }{ 2 } $

  2. $\dfrac { \sqrt { 3 } }{ 2 } A\pi $

  3. $A\pi $

  4. zero

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Correct Option: C

Two strings of same material are stretched to the same tension. If their radii are in the ratio $1:2$, then respective wave velocities in them will be in ratio

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

  1. $4:1$

  2. $2:1$

  3. $1:2$

  4. $1:4$

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Correct Option: B
Explanation:
We know that the velocity of wave in a stretched string is given by:
$v=\sqrt{\dfrac{TL}{m}}$
Where $T=$tension$=$same for both
$L=$length$=$same for both
$m=$mass
hence
$v\propto \dfrac{1}{\sqrt{m}}$
we know that
mass$=$volume$\times$ density
$=\pi r^2L\rho$
Since L and $\rho$ are equal for both the strings, hence $m\propto r^2$
$\Rightarrow v\propto \dfrac{1}{\sqrt{m}}\propto \dfrac{1}{r}$
$\Rightarrow \dfrac{v _1}{v _2}=\dfrac{r _2}{r _1}=2:1$.

The equation of a ware is represented by $y = {10^4}\,\sin \,\left[ {100t - \frac{X}{{10}}} \right]$ here $X$ in meter and $t$ in second$.$ The velocity of the wave will be $:-$

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

  1. $100 m/s$

  2. $250 m/s$

  3. $750 m/s$

  4. $1000 m/s$

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Correct Option: D

A stretched string is $1\ m$ long. Its liner density is $0.5\ gm/m$. It is stretched with a force of $20\ N$. If plucked at a distance of $25\ cm$ from one end, the frequency of the tone emitted by it is

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

  1. $100\ Hz$

  2. $200\ Hz$

  3. $300\ Hz$

  4. $400\ Hz$

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Correct Option: B

A particle moves with simple harmonic motion in a straight line. In first $\tau s,$, after starting from rest it travels a distance $a$, and in next $\tau s$ it travels $2a$, in same direction, then:

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

  1. amplitude of motion is $4a$

  2. time period of oscillations is $6$,

  3. amplitude of motion is $3a$$\tau $

  4. time period of oscillations is $8$,$\tau $

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Correct Option: A

An elastic string carrying a baby of mass 'm' extends by 'e' . The body rotates in a vertical circle with critical velocity. The externsion in the string at the lowest position is 

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

  1. $2e$

  2. $4e$

  3. $6e$

  4. $8e$

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Correct Option: C

The equation of a progressive wave for a wire is: 
$Y=4\sin{\left[\cfrac{\pi}{2}\left(8t-\cfrac{x}{8}\right)\right]}$. If $x$ and $y$ are measured in cm then velocity of wave is :

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

  1. $64 cm/s$ along $-x$ direction

  2. $32 cm/s$ along $-x$ direction

  3. $32 cm/s$ along $+x$ direction

  4. $64 cm/s$ along $+x$ direction

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Correct Option: D
Explanation:

$\begin{array}{l} w=4\pi  \ K=\dfrac { \pi  }{ { 16 } }  \ v=\dfrac { w }{ K } =64\, m/s\, along\, \, +x-axis \ Hence, \ option\, \, D\, \, is\, correct\, \, answer. \end{array}$

An open tube is in resonance with string (frequency of vibration of tube in $n _{0}$. If tube is dipped on water is that 75% of length of tube is inside water, then the ratio of the frequency of tube to string now will be 

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

  1. 1

  2. 2

  3. $\dfrac{2}{3}$

  4. $\dfrac{3}{2}$

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Correct Option: B
Explanation:
For open tube no $ = \dfrac{V}{2l} $
For closed tube length available for resonance
$ l^{1} ,l\times \dfrac{25}{100} = \frac{l}{4} $
fundamental frequency of water filled tube 
$ n _{1}\dfrac{V}{4l^{1}} = \frac{V}{4(l/4)} $ $(\because l^{1}= l/4) $
$ \therefore \dfrac{V}{l} = 2n _{0} = 1 $
$ = \dfrac{n}{n _{0}} = 2 $

The equation of a standing wave in a string fixed at both ends is given as $ y =  A \quad sin \quad  kx \quad cos \quad \omega t $
The amplitude and frequency of a particle vibrating at the mid of an antiode and a node are respectively

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

  1. $A,\dfrac{\omega }{{2\pi }}$

  2. $\dfrac{A}{{\sqrt 2 }},\dfrac{\omega }{{2\pi }}$

  3. $A,\dfrac{\omega }{{\pi }}$

  4. $\sqrt 2 A,\dfrac{\omega }{{2\pi }}$

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Correct Option: A

A wire of length l , area of cross section A  and young's modules of elasticity  y is  suspended from the roof of a building. A  block of mass m is attached at lower end of the wire. if the block is displaced from its mean position and then released the block starts  oscillating. Time period of these oscillation will be

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

  1. $2\pi \sqrt { \frac { Al }{ mY } } $

  2. $2\pi \sqrt { \frac { AY }{ ml } } $

  3. $2\pi \sqrt { \frac { ml }{ YA } } $

  4. $2\pi \sqrt { \frac { m }{ YAl } } $

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Correct Option: B