Tag: physics

Questions Related to physics

Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by $45^o$, then.

resonance oscillations physics

  1. The resultant amplitude $(1+\sqrt{2})a$

  2. The phase of the resultant motion relative to the first is $90^o$

  3. The energy associated with the resulting motion is $(3+2\sqrt{2})$ times the energy associated with any single motion

  4. The resulting motion is not simple harmonic

Show answer
Correct Option: A,C
Explanation:

Let $y _1=a\sin \left(\omega t-\cfrac {\pi}{4}\right)$
$y _2=a\sin (\omega t)$
$y _3=a\sin \left(\omega t+\cfrac {\pi}{4}\right)$
On super imposing, resulting SHM-
$y=a\left[\sin \left(\omega t-\cfrac{\pi}{4}\right)+\sin \omega t+\sin \left (\omega t+\cfrac {\pi}{4} \right)\right]$
$\implies y=a \left[2\sin \omega t\cos \cfrac {\pi}{4}+\sin \omega t\right]$
$\implies y=a(1+\sqrt {2})\sin \omega t$
$\therefore$ Resultant amplitude $=(1+\sqrt{2})a$
Also, $\cfrac {E _{resultant}}{E _{single}}=\left(\cfrac {A}{a}\right)^2$
$\implies \cfrac {E _{resultant}}{E _{single}}=(\sqrt{2}+1)^2$
$\implies \cfrac {E _{resultant}}{E _{single}}=(3+2\sqrt{2})$
$\therefore E _{resultant}=(3+2\sqrt{2})E _{single}$

The amplitude of damped oscillator becomes $\dfrac{1}{3}$ in $2\ s$. Its amplitude after $6\ s$ is $1/n$ times the original. The value of $n$ is ?

resonance oscillations physics

  1. $2^{3}$

  2. $3^{2}$

  3. $3^{1/2}$

  4. $3^{3}$

Show answer
Correct Option: D

A cylindrical tube,open at one end and closed at the other,is acoustic unison with an external source of frequency held at the open end of the tube, in its fundamental note. Then:

resonance oscillations physics

  1. The displacement wave from the source gets reflected with a phase change of $ \pi $ at the closed end

  2. The pressure wave from the source get reflected without a phase change at the closed end

  3. The wave reflected from the closed end again gets reflected at the open end

  4. The wave reflected from the closed end does not suffer reflection at the open end

Show answer
Correct Option: A
Explanation:

A cylindrical tube,open at one end and closed at the other,is acoustic unison with an external source of frequency held at the open end of the tube, in its fundamental note, then the displacement wave from the source gets reflected with a phase change of  $\pi $ at the closed end.

so the correct option is A.

For a certain organ pipe open at both ends, the successive resonance frequencies are obtained at $510, 680$ and $850\ Hz$. The velocity of sound in air is $340\ m/s$. The length of the pipe must be:

resonance oscillations physics

  1. $2\ m$

  2. $0.5\ m$

  3. $m$

  4. $0.25\ m$

Show answer
Correct Option: A

Suggest one way by which rattling sound could be stopped.

resonance oscillations physics

  1. Rattling sound can be stopped by changing the speed of the vehicle.

  2. Rattling sound can be stopped by changing the frequency of the vehicle.

  3. Rattling sound can be stopped by changing the vibration of the vehicle.

  4. None of the above.

Show answer
Correct Option: A
Explanation:

The cause of rattling sound is resonance and it can be stopped by changing the speed of the vehicle. 

Some opera singers are able to use their voice to shatter a crystal glass. Which of the phenomenon is used to explain this ? 

resonance oscillations physics

  1. Acoustic reflection

  2. Multiple echoes

  3. Interference

  4. Resonance

  5. Beats

Show answer
Correct Option: D
Explanation:

 When the  external frequency becomes equal to the natural frequency of the body , then the amplitude of vibrations of the body becomes very large , this phenomenon is called resonance .

   When a opera singer  manages his frequency such that it becomes equal to the natural frequency of crystal glass , resonance occurs and glass shatters.

Equations y = 2A cos$^{2}$ $\omega $t and y = A (sin $\omega $  + $\sqrt{3}$ cos $\omega $t  ) represent the motion of two particles.

resonance oscillations physics

  1. Only one of these is S.H.M.

  2. Ratio of maximum speeds is 2 : 1

  3. Ratio of maximum speeds is 1 : 1

  4. Ratio of maximum accelerations is 1 : 4

Show answer
Correct Option: C

Your friend is playing a song on a piano. Whenever your friend hits a certain key, the lamp on top of the piano rattles. Explain why the lamp rattles.

resonance oscillations physics

  1. The lamp rattles because of the occurring of interference 

  2. The lamp rattles because of the occurring of diffraction 

  3. The lamp rattles because of the occurring of resonance

  4. None of the above 

Show answer
Correct Option: C
Explanation:

This happens due to resonance (A phenomenon in which a vibrating system or external force drives another system to oscillate with a greater amplitude at a specific frequency). The lamp on top of the piano has a resonant frequency equal to one of the notes being played.

During resonance, sound waves tend to absorb

resonance oscillations physics

  1. more energy

  2. less energy

  3. no energy

  4. infinite energy

Show answer
Correct Option: A
Explanation:

System to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies.

A glass tube of $1.0 m$ length is filled with water. The water can be drained out slowly at bottom of the tube. If a vibrating turning fork of frequency $500 Hz$ is brought at the upper end of the tube and the velocity of sound is $330 \,\,m\,\,s^{-1}$, then the total number of resonances obtained will be:

resonance oscillations physics

  1. 4

  2. 3

  3. 2

  4. 1

Show answer
Correct Option: B
Explanation:

Wavelength of the sound produced is,
$\lambda = \dfrac{Velocity}{Frequency} $


$= \dfrac{330\,\,m\,\,s^{-1}}{500\,\,s^{-1}} = 0.66\,\,m$
The resonance occurs at
$\dfrac{\lambda}{4},\dfrac{3\lambda}{4},\dfrac{5\lambda}{4},\dfrac{7\lambda}{4},.....$
i.e., at $0.165\,\,m, 0.495\,\,m, 0.825\,\,m, 1.155\,\,m$. As the length of the tube is only $1.0\,\,m$, hence $3$ resonance will be observed.