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Resonance - class-XI

Description: resonance
Number of Questions: 20
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Tags: oscillations physics
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A resonance tube is resonated with tuning fork of frequency 256 Hz. If the length of first and second resonating air columns are 32 cm and 100 cm, then end correction will be 

resonance oscillations physics

  1. $1 cm$

  2. $2 cm$

  3. $4 cm$

  4. $6 cm$

Show answer
Correct Option: B

If $\omega _{0}$ is natural frequency of damped forced oscillation and $p$ that of driving force, then for amplitude resonance

resonance oscillations physics

  1. $p _{r}= \omega _{0}$

  2. $p _{r}< \omega _{0}$

  3. $p _{r}> \omega _{0}$

  4. $p _{r}> = \omega _{0}$

Show answer
Correct Option: A

Which of the following is an example of mechanical resonance?

resonance oscillations physics

  1. A child on a swing.

  2. A pendulum.

  3. A tuning fork.

  4. Nuclear magnetic resonance

Show answer
Correct Option: A,B
Explanation:

$Answer:-$ A,B

Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings and airplanes—a phenomenon known as resonance disaster.

Various examples of mechanical resonance include:-

  • Most clocls keep time by mechanical resonance in a balance wheel, pendulum, or quartz crystal.
  • The resonance of the basilar membranein the ear.
  • Making a child's swing swing higher by pushing it at each swing.
  • A wineglass breaking when someone sings a loud note at exactly the right pitch.

 A mechanical system is oscillating at resonance with a constant amplitude. Which one of the following statements is not correct?

resonance oscillations physics

  1. The applied force prevents the amplitude from becoming too large.

  2. The frequency of the applied force is the same as the natural frequency of oscillation of the system.

  3. The total energy of the system is constant.

  4. The amplitude of oscillations depends on the amount of damping.

Show answer
Correct Option: A
Explanation:

The applied force prevents the amplitude from becoming too large.


Option A is correct.

Which of the following is an example of acoustic resonance?

resonance oscillations physics

  1. Feedback in guitars

  2. A pendulum

  3. Nuclear magnetic resonance

  4. A swing

Show answer
Correct Option: A
Explanation:

$Answer:-$ A

Acoustic resonance is a phenomenon that consists of a given acoustic system amplifying a sound whose frequency matches one of its own natural frequencies of vibration (its resonance frequencies).
The resonance of a tube of air is related to the length of the tube, its shape, and whether it has closed or open ends. Musically useful tube shapes are conical and cylindrical . A pipe that is closed at one end is said to be stopped while an open pipe is open at both ends. Modern orchestral flutes behave as open cylindrical pipes; clarinets and lip-reed instruments (brass instruments) behave as closed cylindrical pipes; and saxophones, bassoons as closed conical pipes. Vibrating air columns also have resonances at harmonics, like strings (in guitars).

Destruction of buildings during an earthquake is an example of:

resonance oscillations physics

  1. mechanical resonance

  2. beats

  3. damped vibration

  4. critical vibration

Show answer
Correct Option: A
Explanation:

During earthquake, when the frequency of earthquake becomes equal to the natural frequency of building, resonance (mechanical) occurs due to which amplitude of vibration of building increases and building get destroy.

Which of the following shows mechanical resonance?

resonance oscillations physics

  1. Balance wheel

  2. Pendulum

  3. Quartz crystal

  4. All of the above

Show answer
Correct Option: D
Explanation:

$Answer:-$ D

Mechanical resonance is the tendency of a mechanicalsystem to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies.
examples: Most clocks keep time by mechanical resonance in a balance wheel, pendulum, or quartz crystal.

Which of the following shows acoustic resonance?

resonance oscillations physics

  1. Harps

  2. Guitars

  3. Pianos

  4. Crystal quarts

Show answer
Correct Option: A,B,C
Explanation:

$Aswer:-$ A,B,C

Acoustic resonance is a phenomenon that consists of a givenacoustic system amplifying a sound whose frequency matches one of its own natural frequencies of vibration (its resonancefrequencies).
Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane.
In quartz crystals mechanical resonance occurs.

Pushing a person in a swing is a common example of which type of resonance?

resonance oscillations physics

  1. Mechanical resonance

  2. Acoustic resonance

  3. Tidal resonance

  4. None of the above

Show answer
Correct Option: A
Explanation:

When we push a person in a swing, we generally match the time between two consecutive pushes, with the time, in which swing comes back to its extreme position. In fact we match our pushing frequency with the frequency of swing to get large arc of swing (amplitude), this is a common example of mechanical resonance.

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.

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