Tag: oscillations and waves

Questions Related to oscillations and waves

Two identical light waves, propagating in the same direction, have a phase difference $\delta $. After they superpose the intensity of the resulting wave will be proportional to

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $\cos { \delta } $

  2. $\cos { \left( \dfrac { \delta }{ 2 } \right) } $

  3. $\cos ^{ 2 }{ \left( \dfrac { \delta }{ 2 } \right) } $

  4. $\cos ^{ 2 }{ \delta } $

Show answer
Correct Option: C
Explanation:

Maximum intensity,
     $I=4{ I } _{ 0 }\cos ^{ 2 }{ \left( \dfrac { \delta  }{ 2 }  \right)  } $
$\Rightarrow I\propto \cos ^{ 2 }{ \left( \dfrac { \delta  }{ 2 }  \right)  } $

In the Young's double slit experiment, the resultant intensity at a point on the screen is 75% of the maximum intensity of the bright fringe. Then the phase difference between the two interfering rays at that point is 

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $\frac {\pi}{6}$

  2. $\frac {\pi}{4}$

  3. $\frac {\pi}{3}$

  4. $\frac {\pi}{2}$

Show answer
Correct Option: C
Explanation:

The correct answer is option(C).

We know, The resultant intensity,
$I _R=4I _{max}cos^2\left( \frac \phi 2\right)$
$or, cos^2\left( \frac \phi 2\right)=\frac {I _R}{4I _max}=\frac {0.75}4=0.1875$
$\Rightarrow cos\left(\frac \phi 2\right)=\sqrt {0.1875}=0.5$
$\Rightarrow \frac \phi 2 = cos _{-1}(0.5)=\frac \pi 3$

Two beams of light having intensities I and 4 I interface to produce a fringe pattern on a screen. The phase difference between the beams is $\dfrac { \pi  }{ 2 }$ at point A and $\pi$ at point B, Then the difference between the resultant intensities at A and B is

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. 2 I

  2. 4 I

  3. 5 I

  4. 7I

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Correct Option: B
Explanation:

Resultant intensity at a point, $I _R= I _1+ I _2 +2\sqrt{I _1I _2} cos \phi$

where $I _1$ and $I _2$ be the intensities of two sources and $\phi$ be the phase differences of the sources at that point.
Here, $I _1= I$ and $I _2=4I$

At point $A$, $\phi= \dfrac{\pi}2$
So,Resulant intensity at point $A$,   $I _A= 5I+ 2\sqrt{4I^2}cos \dfrac{\pi}2= 5I$   

At point $B$, $\phi=\pi$

So,Resulant intensity at point $B$,   $I _B= 5I+ 2\sqrt{4I^2}cos\pi= 5I-4I= I$

Hence, Required difference between the intensities at $A$ and $B= I _A-I _B= 5I-I= 4I$

In Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same arrangement, the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is $I _1$ and in the second case is $I _2$, then the ratio $I _1/I _2$ is: 

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. $0.5$

  2. $4$

  3. $2$

  4. $1$

Show answer
Correct Option: A

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen.If the phase difference between the beams is $\dfrac{\pi }{2}$ at point A and $\pi$ at point B then the difference between the resultant intensities at A and B is 

multiple-slit diffraction the principle of superposition of waves superposition of waves oscillations and waves physics

  1. 4I

  2. 2I

  3. 5I

  4. 7I

Show answer
Correct Option: A
Explanation:

The resultant intensity is given by:
$I={I} _{1}+{I} _{2}+2\sqrt{{I} _{1}{I} _{2}}\cos{\phi}$
Thus difference is given by:
${I} _{A}-{I} _{B}=2\sqrt{{I} _{1}{I} _{2}}(\cos{\dfrac{\pi}{2}}-\cos{\pi})=2\sqrt{4{I}^{2}}\times1=4I$

A string is under tension so that its length is increased by $1/n$ times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. $1:n$

  2. ${n}^{2}:1$

  3. $\sqrt{n}:1$

  4. $n:n+1$

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Correct Option: D

Motion that moves to and fro in regular time intervals is called _________________ motion.

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. Vibratory

  2. Translatory

  3. Rotatory

  4. Accelerating

Show answer
Correct Option: A
Explanation:

Sounds are made by vibrations. Some vibrations are easy to see. The vibrations that create sound must travel through a medium, such as air or water, or anything made of molecules. With each forward motion, air molecules pulse outward, pushing other air molecules and crowding them together. With each backward motion, the molecules get less crowded. The forward and backward vibration of the glass creates a chain reaction of crowded and not-so-crowded molecules that ripples through the air. This traveling vibration is called a sound wave. 
Motion that moves to and fro in regular time intervals is called vibratory or oscillatory motion.

When we hear a sound, we can identify its source from : 

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. Amplitude of sound

  2. Intensity of sound

  3. Wavelength of sound

  4. Overtones present in the sound

Show answer
Correct Option: D
Explanation:

Answer is D.

When we hear a sound, we can identify its source from overtones present in the sound.
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.

The vibrations produced by the body after it is into vibration is called ....................

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. Force Vibrations

  2. Free or Natural Vibrations

  3. Damped Vibrations

  4. None of these

Show answer
Correct Option: B

The length of a stretched string is $2 m$. The tension in it and its mass are $10 N$ and $0.80 kg$ respectively. Arrange the following steps in a sequence to find the third harmonic of transverse wave that can be created in the string.
(a) Find the linear mass density ($m$) using the formula, $m$ $\displaystyle = \dfrac{mass (M)  of \ the \  string}{length (l)  of \ the \  string}$
(b) Collect the data from the problem and find the length($l$) tenstion ($T$) and mass ($M$) of the stretched string.
(c) The fundamental frequency of a stretched vibrating string is given by $n$ $=\displaystyle \dfrac{1}{2l} \sqrt{\dfrac{T}{m}}$
(d) The frequency of $2^{nd}$ overtone or $3^{rd}$ harmonic is given by $n _2\displaystyle = \dfrac{3}{2l}\sqrt{\dfrac{T}{m}}=3n$.

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. a b c d

  2. d b c a

  3. b a c d

  4. b d c a

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Correct Option: C
Explanation:

Collect the data from the problem and find the length ($l$), tension ($T$) and mass ($M$) of the stretched string (b). 

Find the linear mass density (m) using the formula, m $= m/l$  (a).
The fundamental frequency of a stretched vibrating string is given by, n $=\displaystyle \dfrac{1}{2l} \sqrt{\dfrac{T}{m}}$ (c).
The frequency of $2^{nd}$ overtone or $3^{rd}$ harmonic is given by $n _2=\displaystyle \dfrac{3}{2l} \sqrt{\dfrac{T}{m}}=3n$ (d)