Tag: wave motion

Questions Related to wave motion

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. $5mg/ 2$

Show answer
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. $0.0054 N$

Show answer
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. $4 m$

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

Show answer
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. $4th$

Show answer
Correct Option: B

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

Show answer
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. $1:4$

Show answer
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. $1000 m/s$

Show answer
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. $400\ Hz$

Show answer
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 $

Show answer
Correct Option: A