Tag: resonance

Questions Related to resonance

State whether the given statement is True or False :

Resonance is the cause of sound production in musical instruments.

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:

Resonance is cause of sound production in musical in instrument. this statement is true. Generally musical instrument have a hollow chamber, it contains air particle. when vibration is produced, it may be in the objects attached to it, the frequency of this object may match with a natural frequency of air particle inside the hollow chamber. Thus the air particles start to vibrate with the large amplitude which produces large sound. 

Resonance occurs when a vibrating system or external force drives another system to ____ with greater _ at a specific preferential ______. Fill in the blanks. 

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

  1. oscillate, amplitude, frequency

  2. oscillate, frequency, amplitude

  3. vibrate, velocity, frequency

  4. vibrate, frequency, velocity

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Correct Option: A
Explanation:

$Answer:-$ A

In physics, resonance is a phenomenon that occurs when a given system is driven by another vibrating system or external force to oscillate with greater amplitude at a specific preferential frequency.

Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequencyof the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.
Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance(NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters).

In a resonance tube with tuning fork of frequency $512 \ Hz$, first resonance occurs at water level equal to $30.3 \ cm$ and second resonance occurs at $63.7 \ cm$. The maximum possible error in the speed of sound is

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

  1. $51.2 \ cm/s$

  2. $102.4 \ cm/s$

  3. $204.8 \ cm/s$

  4. $153.6 \ cm/s$

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Correct Option: C
Explanation:

$\begin{array}{l} { l _{ 1 } }+e=\frac { V }{ { 4f } } \to \left( i \right)  \ { l _{ 2 } }+e=\frac { { 3V } }{ { 4f } } \to \left( { ii } \right)  \ Sub\, \, \left( { ii } \right) \, \, & \, \, \left( i \right)  \ { l _{ 2 } }-{ l _{ 1 } }=\frac { { 2V } }{ { 4f } }  \ { l _{ 2 } }-{ l _{ 1 } }=\frac { V }{ { 2f } }  \ \frac { { \Delta \left( { { l _{ 2 } }-{ l _{ 1 } } } \right)  } }{ { { l _{ 2 } }-{ l _{ 1 } } } } =\frac { { \Delta V } }{ V }  \ \Delta V=2f\Delta \left( { { l _{ 2 } }-{ l _{ 1 } } } \right) =2f\left( { \Delta { l _{ 1 } }+\Delta { l _{ 2 } } } \right) ......for\, \, man\, \, error \ =2\times 512\times \left( { 0.1+0.1 } \right) =204.8\, \, cm/s \end{array}$

The phenomenon of resonance is used in receiving the radio and television programmes.

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

  1. True

  2. False

  3. Nither

  4. Either

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Correct Option: A
Explanation:

This is a resonance in the circuit--- when you have a bunch of different

frequencies driving a resonant system, the response is only strong for

those frequencies which are close to the natural frequency of the

resonant oscillator. The frequency dependent amplification  is used to done through the resonance circuit for a desired frequency.

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. $100$ cm from the open end

Show answer
Correct Option: B,D
Explanation:
For $1^{st}$ resonance $(1/4)\lambda =L$
$\Rightarrow \lambda =4L$ ..(i)
For $2$nd resonance
$3\left(\dfrac{\lambda}{4}\right)=L _2\Rightarrow \lambda =\dfrac{4L _2}{3}$ .(ii)
By using (i) and (ii)
$\dfrac{4L _2}{3}=4L _1$
$\Rightarrow L _2=3L _1=3(20)=60$cm
Similarly, $L _3=5L _1=100$ cm
Hence (B) and (D) are correct.

The third overtone of a pipe is found to be in unison with the first overtone of an open pipe. The ratio of lengths of the pipes is 

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

  1. $\dfrac { 3 }{ 4 }$

  2. $\dfrac { 3 }{ 5 }$

  3. $\dfrac { 2 }{ 5 }$

  4. $\dfrac { 7 }{ 4 }$

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Correct Option: D

In case of a forced vibration, the resonance wave becomes very sharp when the

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

  1. restoring force is small

  2. applied force is small

  3. damping is small

  4. quality factor is small

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Correct Option: C
Explanation:

at resonance,the damping force becomes small enough so that the resulting oscillations have large amplitude.

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 $= 1\ cm)$.

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

  1. $5\ cm$

  2. $10\ cm$

  3. $25\ cm$

  4. $20\ cm$

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Correct Option: A

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

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

  1. 200 cm

  2. 202 cm

  3. 203 cm

  4. 204 cm

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Correct Option: C
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.

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. $4$

Show answer
Correct Option: A
Explanation:

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

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

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

$n = 1$