Tag: resonance: examples and uses

Questions Related to resonance: examples and uses

A organ pipe open on both ends in the $n^{th}$ harmonic is in resonance with a source of $1000 \,Hz$. The length of pipe is $16.6 \,cm$ and speed of sound in air is $332 \,m/sec$. Find the value of $n$.

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: A
Explanation:

$f = \dfrac{nV}{2\ell}$

$1000 = \dfrac{n \times 332}{2 \times 16.6 \times 10^{-2}}$

$10 = \dfrac{n \times 332}{33.2}$

$n = 1$

In a forced harmonic oscillator of natural frequency $\omega _0$, the resonant frequency $\omega _r$ is

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

  1. $>\omega _0$

  2. $<\omega _0$

  3. $=\omega _0$

  4. not related to $\omega _0$

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Correct Option: C
Explanation:

The resonant frequency is always equal to natural frequency, hence option C is correct.

Resonance is a special case of $\underline{           }$ vibrations, when frequency of the driving force is$\underline{           }$ natural frequency of the body.

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

  1. forced, equal to the

  2. particle , more then the

  3. wave, equal to the

  4. forced, less than the

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Correct Option: A
Explanation:

Resonance is a special case of forced vibrations, when frequency of the driving force is equal to the natural frequency of the body.
Resonance is the result of an external force vibrating at the same frequency as the natural frequency of a system. Natural frequency is a characteristic of every machine, structure and even animals. Often, resonance can be confused with the natural frequency or critical frequency. If equipment is operating in a state of resonance, the vibration levels will be amplified significantly, which can cause equipment failure and plant downtime. It is, therefore, important that the running speed of equipment be out of the resonance range.

A forced oscillator is acted upon by a force $F={ F } _{ \circ  }sin\omega t.$. The amplitude of oscillation is given by $\displaystyle\frac{55}{\sqrt{2\omega^2 - 36\omega + 9}}$. The resonant angular frequency is

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

  1. $2\space unit$

  2. $9\space unit$

  3. $18\space unit$

  4. $36\space unit$

Show answer
Correct Option: B
Explanation:

At resonance, amplitude of oscillation is maximum
$\quad \Rightarrow 2\omega^2 - 36\omega + 9$ is maximum
$\quad \Rightarrow 4\omega - 36 = 0$ (derivative is zero)
$\quad \Rightarrow \omega = 9$

Imagine a child sitting on a swing in a park and the child's mother is pushing the swing from the back. The mother maintains the same tempo as the motion of the swing. If the mother tries to push at a faster tempo, the arc of the swing will:

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

  1. increase

  2. decrease

  3. remain the same

  4. become zero, i.e., the swing will stop

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Correct Option: B
Explanation:

As the mother maintains the same tempo as the motion of the swing, it means frequency of mother and the swing is same, there is resonance. When mother tries to push at a faster tempo, frequency of mother changes and resonance is disturbed due to which, the arc of swing (amplitude) decreases.

A vibrating object will pick out its __________ from a complex excitation and vibrate at those frequencies.

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

  1. resonant frequency

  2. natural frequency

  3. both

  4. none

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Correct Option: A
Explanation:

A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

State whether the given statement is True or False :
By tuning ultra sound waves to the natural frequency of a kidney stone, we can rely on resonance to pulverize the stone.

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:

By turning ultrasound waves to the natural frequency of a kidney stone, we rely on resonance to parcels which the stones consist of vibrate with large amplitude and at a certain moment, this vibration causes breakdown of stone into pieces. So the given statement is true.

Which one does not work on principles of resonance?

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

  1. T.V

  2. Radio

  3. Microwave oven

  4. Bulb

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Correct Option: D
Explanation:

Resonance in an electrical circuit is a phenomenon in which the inductive reactance and the capacitive reactance become equal and cancel each other.

As a result, the impedance of the circuit becomes the least and maximum current flows through the circuit. This happens only at a particular frequency of the AC power supply, known as resonant frequency. 
All the devices except bulb work on this principle. The circuit in them is tuned in order to make their resonant frequency matching with the desired one. This is done by adjusting the values of the inductor or the capacitor.
In a bulb, there is only pure resistance and no reactive component. There is no question of resonance.

In a resonance column experiment, the first resonance is obtained when the level of the water in tube is $20 cm$ from the open end. Resonance will also be obtained when the water level is at a distance of

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

  1. $40 cm$ from the open end.

  2. $60 cm$ from the open end.

  3. $80 cm$ from the open end.

  4. data insufficient.

Show answer
Correct Option: B
Explanation:

In a closed pipe : length of the pipe is length of the air column in fundamental.

$\dfrac { \lambda  }{ 4 } =20cm$ 
${ 2 }^{ nd }$ harmonic resonance $=\dfrac { 3\lambda  }{ 4 } =3\times 20=60cm$

$\therefore $  Option (B) is correct.

Assertion : In the ideal case of zero damping, the amplitude of simple harmonic motion at resonance is infinite.
Reason : All real systems have some damping.

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

  1. If both assertion and reason are true and reason is the correct explanation of assertion.

  2. If both assertion and reason are true and reason is not the correct explanation of assertion.

  3. If assertion is true but reason is false.

  4. If both assertion and reason are false.

Show answer
Correct Option: B
Explanation:

If there was no damping in the swing, the swing would move with larger and larger amplitudes. However, most physical systems have damping, which limits the size of the amplitude. If you don not have damping the amplitudes will go to infinity.

So, Assertion and reason both are true. But reason is not current explanation for the assertion.