Tag: resonance

Questions Related to resonance

Two understand oscillators are known to have the same neutral frequency $ \omega _0 $ . The mass and damping coefficient of the first oscillator are $m _1 $ and $b _1 $ , and the mass and damping coefficient of the second oscillator are $m _2 $ and $b _2$ , respectively. A sinusoidal driving force of $F _{ext} = F _0 \cos \omega t $ is applied to each oscillator. Starting with $\omega $ far from $ \omega _0$ the driving force is tuned in order to observe resonant behavior. If $ m _1 = 4 m _2 $ and $b _1 = 2b _2 $ , then which one the following statements concerning the driven oscillations is correct?

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. The resonant peak of the first driven oscillator is higher and narrower than that of the second oscillator.

  2. The resonant peak of the first driven oscillator is higher and wider than that of the second oscillator.

  3. The resonant peak of the first driven oscillator is lower and wider than that of the second oscillator.

  4. The resonant peak of the first driven oscillator is lower and narrower than that of the second oscillator.

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Correct Option: A

A student is performing the experiment of resonance Column. The diameter of the column tube is $4\ cm$. The frequency of the tuning fork is $512\ Hz$. The air temperature $38^{o}C$ in which the speed sound is $336\ m/s$. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is:

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. $14.0\ cm$

  2. $15.2\ cm$

  3. $16.4\ cm$

  4. $17.6\ cm$

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Correct Option: B
Explanation:

For $I^{st}$ resonance

$l _1 + e = \dfrac{\lambda}{4}$ or $l _1 = \dfrac{\nu}{4f} - 0.3d = 15.2\space cm$

The example of forced vibration is

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. resonance.

  2. beats.

  3. interference.

  4. diffraction.

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Correct Option: A
Explanation:

when one object vibrating at the same natural frequency of a second object forcesis called resonance.

so that correct option is A.

Amplitude of a wave is represented by  $A=\frac{c}{a+b-c}$ Then resonance will occur when

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. b = -c/2

  2. b = 0 and a = c

  3. b = - a/2

  4. None of these

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Correct Option: B
Explanation:

$A=\dfrac{c}{a+b-c}$ : When  b = 0, a = c
Amplitude $A\rightarrow \infty$. This corresponds to resonance

If two vibrating systems are in resonance, then :

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. Their amplitudes are equal

  2. Their frequencies are equal

  3. Their temperatures are equal

  4. Their intensities are equal

Show answer
Correct Option: B
Explanation:

Answer is C.

Resonance is a phenomenon that consists of a given system being driven by another vibrating system or by external forces to oscillate with greater amplitude at some preferential frequencies. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. 
When both the bodies vibrate, they will start to vibrate with the same frequency.

State whether the given statement is True or False :
One example of resonance involving visible and invisible light in the electromagnetic spectrum is resonance fluorescence. 

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. True

  2. False

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Correct Option: A
Explanation:

One example of resonance involving visible and invisible light in the electromagnetic spectrum is resonance fluorescence. Fluorescence itself is a process whereby a material absorbs electromagnetic radiation from one source, then re-emits that radiation on a wavelength longer than that of the illuminating radiation. 

Among its many applications are the fluorescent lights found in many homes and public buildings. Sometimes the emitted radiation has the same wavelength as the absorbed radiation, and this is called resonance fluorescence.
Resonance fluorescence is used in laboratories for analyzing phenomena such as the flow of gases in a wind tunnel.

Resonance is exhibited in 

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. quartz crystals

  2. clocks

  3. ear membranes

  4. pendulum

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Correct Option: A,B,C,D
Explanation:

$Answer:-$ A,B,C,D

Various examples of mechanical resonance include:

  • Most clocks keep time by mechanical resonance in a balance wheel,pendulum, or quartz crystal.
  • Orbital resonance as in some moons of the solar system's gas giants.
  • The resonance of the basilar membrane in 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.

What conditions are necessary to produce resonance in an object?

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. The object must have at least one natural frequency of vibration.

  2. The object must be driven by an external vibrating force.

  3. The frequency of the external vibrating force must match the object's natural frequency of vibration.

  4. All of the above.

Show answer
Correct Option: D
Explanation:

Resonance is a phenomenon in which the periodic oscillatory force acting on an object has a frequency of vibration same as the natural frequency of the object. In this, the object vibrates with a large amplitude.

Pick the wrong statement:

Interference to occur:

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. frequency of one wave should be equal to another

  2. amplitude of one wave should be comparable to that of another

  3. one wave must superpose on another

  4. frequency of two waves can never be same / equal

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Correct Option: D
Explanation:

Interference is a phenomenon in which two waves of equal frequencies and nearly equal amplitudes superpose on one another and produce a resultant new wave.

If a singer could match the natural frequency of the wine glass, he:

physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

  1. can shatter the glass

  2. can still never shatter the glass

  3. can at most vibrate the glass

  4. can leave no effect on the glass

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Correct Option: A
Explanation:

$Answer:-$ A 

If a singer could match the natural frequency of the wine glass than he could possibly shatter the glass as coming into resonance would make every atomic particle of glass to vibrate and thereby increasing distance between two particles and hence can actually break.