Tag: speed and acceleration of travelling wave

Questions Related to speed and acceleration of travelling wave

Two wave pulses travel in opposite directions on  a string and approach each other. The shape of one pulse is inverted with respect to the other.

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

  1. The pulse will collide with each other and vanish

    after collision.

  2. The pulses will reflect each other, that is pulse

    going towards right will finally move towards left

    and vice versa.

  3. The pulses will pass through each other but their

    shapes will be modified.

  4. The pulses will pass through each other without

    any change.

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Correct Option: D

If 'v' is the velocity of sound in a gas then 'v' is directly proportional to (where M, d and T represents molecular weight of gas, density of gas and its temperature respectively.)

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

  1. $\sqrt{M}$

  2. $\displaystyle \frac{1}{\sqrt{d}}$

  3. $\sqrt{T}$

  4. Both (2) and (3)

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Correct Option: D

 Standing waves are generated on string laded with a cylindrical body. If the cylinder immersed in water, the length of the loops changes by a factor of 2.2. The specific gravity of the material of the cylinder is 

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

  1. 1.11

  2. 2.15

  3. 2.50

  4. 1.26

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Correct Option: A

In a string the speed of wave is 10 m/s and its frequency is 100 Hz . The value of the phase difference at a distance 2.5 cm will be :

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

  1. ${ \pi }/{ 2 }$

  2. ${ \pi }/{ 8 }$

  3. ${ 3\pi }/{ 2 }$

  4. ${ 2\pi }$

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Correct Option: A
Explanation:

Speed of wave $(v) = 10 m/s$

Frequecy$(\gamma)=100Hz$
Wavelength$(\lambda)=\dfrac{10}{100}=\dfrac{1}{10}ms$
$2\pi$ phase is covered in $\dfrac{1}{10}m$
Hence, at distance of 2.5 m, the phase is $\dfrac{2\pi \times 0.025}{0.1}=\dfrac{\pi}{2}$



A string of mass $3$kg is under tension of $400$N. The length of the stretched string is $25$cm. If the transverse jerk is stuck at one end of the string find the velocity?

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

  1. $25 \pi^2 m s^{-2}$

  2. $-5 \pi^2 m s^{-2}$

  3. $5 \pi^2 m s^{-2}$

  4. $-25 \pi^2 m s^{-2}$

Show answer
Correct Option: B
Explanation:

Here, A = $5cm = 0.05$m, T = $0.2$s


$\therefore \omega = \dfrac{2 \pi}{T} = \dfrac{2 \pi}{0.2} = 10 \pi rad s^{-1}$

Velocity and acceleration of the particle executing SHM at any displacement xi given by

Velocity, $v = \omega \sqrt{A^2 - x^2}$
and acceleration, $a = - \omega^2 x$
when $x = 5 cm = 0.05$m
$\therefore v = 10 \pi \sqrt{(0.05)^2 - (0.05)^2} = 0 and a = - (10 \pi)^2(0.05) = -5 \pi^2 m s^{-2}$

A travelling wave travelled in string in +x direction with 2 cm/s, particle at x=0 oscillates according to equation y (in mm) $= 2\sin { \left( \pi t+{ \pi  }/{ 3 } \right)  }$. What will be the slope of the wave at x=3 cm and t=1 s

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

  1. $-\sqrt { 3 } { \pi }/{ 2 }$

  2. $\tan ^{ -1 }{ \left( -\sqrt { 3 } { \pi }/{ 2 } \right) }$

  3. $-\sqrt { 3 } { \pi }/{ 20 }$

  4. $-\sqrt { 3 } { \pi }$

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Correct Option: A

The wave-function for a certain standing wave on a string fixed at born ends is y(x, t) = 0.5 sin (0.025$\pi$x) cos 500 t where x and y are in centimeters and t is in seconds The shortest possible length of the string is

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

  1. 126 cm

  2. 160 cm

  3. 40 cm

  4. 80 cm

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Correct Option: A
Explanation:
$\phi \vec { B } .\vec { dl } ={ \mu  } _{ 0 }{ I } _{ enclosed }$.
Inside the hollow pipe, ${ I } _{ enclosed }=0$.
$\therefore$   $\phi \vec { B } .\vec { dl } =0$
$\Rightarrow$  $B=0$ inside the pipe $\longrightarrow \left( A \right) $.

A stretched wire emits a fundamental note of $256 Hz$. Keeping the stretching force constant and reducing the length of wire by $10 cm$, the frequency becomes $320 Hz$, the original length of the wire is:

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

  1. $100 cm$

  2. $50 cm$

  3. $400 cm$

  4. $200 cm$

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Correct Option: B
Explanation:

frequency of fundamental note, $\upsilon = \dfrac{1}{2L} \sqrt{\dfrac{T}{m}}$

In first case, $256 = \dfrac{1}{2L} \sqrt{\dfrac{T}{m}} $                ......(i)

In second case, $320 =\dfrac{1}{2(L - 10)} \sqrt{\dfrac{T}{m}}$    ......(ii)

dividing (ii) and (i) we get,

$\dfrac{320}{256} = \dfrac{2L}{2(L - 10)}$ or $\dfrac{L}{L - 10} = \dfrac{5}{4}$


$\therefore L = 50 cm$

A uniform wire of length 20 m and weighing 5 kg hangs vertically. If g=10 $ms^{-2}$, then the speed of transverse waves in the middle of the wire is

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

  1. $10 ms ^{-1}$

  2. $10\sqrt2 ms ^{-1}$

  3. $15ms ^{-1}$

  4. $2 ms ^{-1}$

Show answer
Correct Option: A
Explanation:

Given,

$m=5kg$
$l=20m$
$\mu=\dfrac{m}{l}=\dfrac{5}{20}=0.25kg/m$
$g=10m/s^2$
Tension in the middle of the wire, $T=\dfrac{m}{2}g$
$T=\dfrac{5}{2}\times 10=25N$
Velocity, $v=\sqrt{\dfrac{T}{\mu}}$
$T=\sqrt{\dfrac{25}{0.25}}=10m/s$
The correct option is A.

The displacement of particles in a string stretched in the $X-$ direction is represented by $y$. Among the following expressions for $y$, those describing wave motion are:

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

  1. $\cos { Kx } \sin { \omega t }$

  2. $-a\cos { \left( Kx-\omega t \right) }$

  3. $-a\cos { \left( Kx+\omega t \right) }$

  4. $-a\sin { \left( Kx-\omega t \right) }$

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Correct Option: A