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Questions Related to physics

A string fixed at one end only is vibrating in its third harmonic. The wave function is $y(x,t) = 0.02 sin(3.13x) cos(512t)$, where y and x are in metres and t is in seconds. The nodes are formed at positions

physics wave motion reflection of waves

  1. (0 m, 2 m)

  2. (0.5 m, 1.5 m)

  3. (0 m, 1.5 m)

  4. (0.5 m, 2 m)

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Correct Option: B
Explanation:

Node in formed only at the finest end of the string and the free end acts as an anti node.

In the third harmonics two nodes are formed:

$y\left( x,t \right) =0.02\sin { \left( 3.13x \right) \cos { \left( 512t \right)  }  } $

Standard equation given by

$y\left( x,t \right) =2a\sin { \left( \cfrac { 2\pi  }{ \lambda  } x \right)  } \cos { \left( 2\pi vt \right)  } $

Comparing both equation, we get

$3.13x\quad =\cfrac { 2\pi  }{ \lambda  } x\\ or,\quad \lambda =\cfrac { 2\lambda  }{ 3.13 } \\ \quad \quad \quad \quad =2 m (approx)$

The nodes are formed at $\cfrac { \lambda  }{ 4 } =0.5$ from origin and at $\cfrac { 3\lambda  }{ 4 } =1.5$ from origin.

 

Two points P and Q are situated at the same distance from a source of light but on opposite sides.The phase difference between the light waves passing through P and Q will be

physics wave optics interference

  1. $\pi$

  2. 2$\pi$

  3. $\pi$/2

  4. 0

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Correct Option: D

Light waves of wave length $\lambda$ propagate in a medium. If $M$ and $N$ are two points on the wave front and they are separated by a distance $\lambda /4$, the phase difference between them will be (in radian)

physics wave optics interference

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

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

  3. $\dfrac{\pi}{45}$

  4. zero

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Correct Option: D

In an interference experiment, distance between the lists is $2\ mm$ and screen is placed at distance $1\ m$ from the slits. Fourth dark fringe is formed exactly opposite to one of the slits. Wavelength of light used in nm is

physics wave optics interference

  1. 480

  2. 600

  3. 570

  4. 500

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Correct Option: A

A glass wedge of angle $0.01$ radian and $\mu=1.5$ is illuminated by monochromatic light of wavelength $6000\ A$ falling normally on it. At what distance from wedge will $10^{th}$ dark fringe be observed by reflected light ?

physics wave optics interference

  1. $0.1\ mm$

  2. $0.2\ mm$

  3. $0.3\ mm$

  4. $0.4\ mm$

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Correct Option: A

In YDSE $S _1$ and $S _2$ has intersity $I$ and $9I$. Find difference in intensity b/w point which has phase difference of  $\pi$

physics wave optics interference

  1. $10 I$

  2. $6 I$

  3. $8I$

  4. $4I$

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Correct Option: D

For interference between waves from two sources of intensities $I$ and $4I$, find the intensity at the point in the pattern where the phase difference is $\dfrac{\pi}{2}$ and $\pi$.

physics wave optics interference

  1. $10I$ and $I$

  2. $5I$ and $5I$

  3. $5I$ and $I$

  4. $5I$ and $10I$

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Correct Option: C

The path difference between two interfering waves at a point on the screen  is $ \lambda /6 $. The ratio of intensity at the point and that the central bright fringe will be (Assume that internally due to each slit in same). 

physics wave optics interference

  1. 0.853

  2. 8.53

  3. 0.75

  4. 7.5

Show answer
Correct Option: C
Explanation:

Given that,

Path difference $x=\dfrac{\lambda }{6}$

We know that,

  $ I={{I} _{0}}{{\cos }^{2}}\left( \dfrac{\phi }{2} \right) $

 $ \dfrac{I}{{{I} _{0}}}={{\cos }^{2}}\left( \dfrac{\phi }{2} \right)....(I) $

Now, the phase difference is

  $ \phi =\dfrac{2\pi }{\lambda }\times x $

 $ \phi =\dfrac{2\pi }{\lambda }\times \dfrac{\lambda }{6} $

 $ \phi =\dfrac{\pi }{3} $

Now, put the value of $\phi $ in equation (I)

  $ \dfrac{I}{{{I} _{0}}}={{\cos }^{2}}{{30}^{0}} $

 $ \dfrac{I}{{{I} _{0}}}=\dfrac{3}{4} $

 $ \dfrac{I}{{{I} _{0}}}=0.75 $

Hence, the value of ratio of the intensity at the point is $0.75$ 

The distance between the two slits in a Young's double slit experiment is $d$ and the distance of the screen from the plane of the slits is $b$,$P$ is a point on the screen directly in front of one of the slits. The path difference between the waves arriving at $P$ from the two slits is

physics wave optics interference

  1. $\dfrac{d^{2}}{b}$

  2. $\dfrac{d^{2}}{2b}$

  3. $\dfrac{2d^{2}}{b}$

  4. $\dfrac{d^{2}}{4b}$

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Correct Option: B

The phase difference between two waves, represented by
${ y } _{ 1 }={ 10 }^{ -6 }sin{ 100t+(x/50)+0.5} m$
${ y } _{ 2 }={ 10 }^{ -6 }cos{ 100t+\left( \frac { x }{ 50 }  \right) } m$
where x is expressed in meters and is expressed in seconds, is approximately:

physics wave optics interference

  1. 2.07 Radians

  2. 0.5 Radians

  3. 1.5 Radians

  4. 1.07 Radians

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Correct Option: D