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

In Resonance tube experiment, if $400\ Hz$ tuning fork is used, the first resonance occurs when length of air column in the tube is $19\ cm$. If the $400\ Hz$. tuning fork is replaced by $1600\ Hz$ tuning fork then to get resonance, the water level in the tube should be further lowered by (take end correction $= 1\ cm)$.

  1. $5\ cm$

  2. $10\ cm$

  3. $25\ cm$

  4. $20\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

The first resonance length of a resonance tube is 40 cm and the second resonance length is 122 cm.third resonance length of the tube will be

  1. 200 cm

  2. 202 cm

  3. 203 cm

  4. 204 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first resonant is$:-$

${L _1} = \frac{\lambda }{4}$
The second resonant length is$:-$
${L _2} = \frac{{3\lambda }}{4}$
the third resonant length of resonance tube is$:-$
${L _5} = 5\,\,\frac{\lambda }{4} = \frac{5}{3}\,\,{L _3} = \frac{5}{3}\left( {122\,cm} \right)$
Hence,
option $(C)$ is correct answer.

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

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 $n$.

  1. $1$

  2. $2$

  3. $3$

  4. $4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

$n = 1$

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

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

  1. forced, equal to the

  2. particle , more then the

  3. wave, equal to the

  4. forced, less than the
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $2\space unit$

  2. $9\space unit$

  3. $18\space unit$

  4. $36\space unit$
Reveal answer Fill a bubble to check yourself
B Correct answer
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)
$\quad \Rightarrow \omega = 9$

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

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:

  1. increase

  2. decrease

  3. remain the same

  4. become zero, i.e., the swing will stop
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. resonant frequency

  2. natural frequency

  3. both

  4. none
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.