Tag: resonance and sonometer

Questions Related to resonance and sonometer

If in an experiment for determination of velocity of sound by resonance tube method using a tuning fork of 512 Hz, first resonance was observed at 30.7 cm and second was obtained at 63.2 cm , then maximum possible error in velocity of sound is ( consider actual speed of sound in air is 332 m/s )

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. $204$ $cm/sec$

  2. $280$ $cm/sec$

  3. $58$ $cm/sec$

  4. $80$ $cm/sec$

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Correct Option: B

Which is(are) the factor(s) on which the frequency of sound emitted due to vibration in an air column depends?

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. Length of air column

  2. Diameter of air column

  3. Both A and B

  4. None of these

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Correct Option: C
Explanation:

In a closed air column, the frequency of mth mode of vibration is given by:

          $f _{m}=\dfrac{v(2m-1)}{4l}$      m=1,2,3......,
In a open air column, the frequency of mth mode of vibration is given by:
          $f _{m}=\dfrac{vm}{2l}$      m=1,2,3......
We can see that frequency depends upon the length of air column $l$ .  
Rayleigh stated that in an air column the antinodes are not formed exactly at the open end, but slightly outside. The distance of the antinode from the antinode is called end correction (e), therefore the length of the air column will change due to end correction hence frequency, this end correction depends upon the radius, r (or diameter) of air column and is equal to $0.6r $.      
Therefore frequency of vibration depends upon on both length and diameter of air column .

The speed of sound waves depends on temperature but speed of light waves does not. Why?

physics stationary waves determining wavelength and speed of sound resonance tube resonance and sonometer

  1. Sound requires medium to travel and light doesn't.

  2. Frequency of sound is less than frequency of light.

  3. Wavelength of sound is larger than wavelength of light.

  4. Speed of sound is smaller than speed of light.

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Correct Option: A

Which of the following can be used to determine the velocity of sound in solids, liquids as well as in gases :

physics stationary waves determining wavelength and speed of sound resonance tube resonance and sonometer

  1. resonance tube

  2. kundt's tube

  3. sonometer.

  4. organ pipe

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Correct Option: B
Explanation:

Kundt's tube is used to determine the velocity of sound in solids, liquids as well as in gases. In Kundt's tube the longitudinal waves are produced in air column and in rod. The nodes are detected by powder particles and the velocity of sound is determined. Also, the sound velocity in liquids is determined using Kundt's tube. The resonance tube, organ pipes are used to determine velocity of sound in air only. And sonometer determines velocity of sound in solids only.  

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonancers are heard at air columns of length $50.7cm$ and $83.9cm$. Which of the following statements is (are) true?

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. The speed of sound determined from this experiment is $332m{s}^{-1}$

  2. The end correction in this experiment is $0.9cm$

  3. The wavelength of the sound wave is $66.4cm$

  4. The resonance at $50.6cm$ corresponds to the fundamental harmonic

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} Let\, \, { n _{ 1 } }\, \, harmonic\, \, is\, \, corresponding\, \, to\, \, 50.7\, cm\, \, and\, \, { n _{ 2 } }\, \, harmonic\, \, is\, \, corresponding\, \, 83.9\, cm. \ { { Sin } }ce\, \, both\, \, one\, \, con\sec  utive\, \, harmonics \ \therefore their\, \, difference=\frac { \lambda  }{ 2 }  \ \therefore \frac { \lambda  }{ 2 } =\left( { 83.9-50.7 } \right) cm \ \frac { \lambda  }{ 2 } =33.2\, cm \ \lambda =66.4\, cm \ \therefore \frac { \lambda  }{ 4 } =16.6\, cm \ length\, \, corresponding\, \, to\, \, fundamental\, \, e\, \, must\, \, be\, \, close\, to\, \, \frac { \lambda  }{ 4 } \, and\, \, 50.7\, cm, \ must\, \, be\, \, and\, \, odd\, \, multiple\, \, of\, \, this\, \, length\, \, 16.6\times 3=49.8\, cm. \ Therefore,\, 50.7\, \, is\, \, { 3^{ rd } }\, \, harmonic \ e+50.7=\frac { { 3\lambda  } }{ 4 }  \ e=49.8-50.7=-0.9\, cm \ speed\, \, of\, \, sound,v=f\lambda  \ \therefore v=500\times 66.4\, cm/\sec  =332\, m/s \end{array}$

Hence,
option $(A)$ is correct answer.

An open pipe of length 33 cm resonates with frequency of 1000 Hz. If the speed of sound s 330 $ms^{-1}$, then this frequency is 

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. The fundamental frequency of the pipe'

  2. The first harmonic of the pipe

  3. The second harmonic of the pipe

  4. The forth harmonic of the pipe

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Correct Option: C
Explanation:

Fundamental frequency (first harmonic frequency) of an open organ pipe is given by ,

                  $n _{1}=v/\lambda=v/2l$ ,
where $v=$speed of sound in air ($=330m/s , given$),
           $\lambda=$ wavelength ,
           $l=$ length of organ pipe ($=33cm=0.33m$  , given) ,
therefore ,  $n _{1}=330/(2\times0.33)=500Hz$ ,
as an open pipe produces even and odd harmonics , and given frequency is 1000Hz , it is 2 times of the first harmonic frequency , therefore it is second harmonic frequency of the pipe .

In a resonance tube the first resonance with a tuning fork occurs at 16 cm and second at 49 cm. If the velocity of sound is 330 m/s, the frequency of tuning fork is :

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. 500 Hz

  2. 300 Hz

  3. 330 Hz

  4. 165 Hz

Show answer
Correct Option: A
Explanation:

For closed pipe $l _1=\dfrac{v}{4n}$
$v=2n(l _2-l _1)$
$n=\dfrac{v}{2(l _2-l _1)}$$=\dfrac{330}{2\times (0.49-0.16)}=500 Hz$

A note has a frequency $128\ Hz$. The frequency of a note two octaves higher than it is

physics stationary waves determining wavelength and speed of sound resonance tube resonance and sonometer

  1. $256\ Hz$

  2. $64\ Hz$

  3. $32\ Hz$

  4. $512\ Hz$

Show answer
Correct Option: D
Explanation:

The sum of the intervals between adjacent notes of the major diatonic scale is an octave.
A series of notes arranged, such that their fundamental frequencies have definite ratios is called a musical scale.
In $1588$, Zarlino constructed a musical scale by introducing six notes between an octave. These eight notes constitute major diatonic scale. The first note or the note of the lowest frequency is called keynote and ratio of the frequencies of the two notes is called interval between them. It means two octaves higher means four times the given frequency.
$\therefore$ Required frequency $=4\times 128$
$= 512\ Hz$

Which of the following is not correct regarding the experiment to determine the velocity of sound in laboratory by resonance tube method?

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. the resonance tube apparatus should be kept inclined

  2. the turning fork should be struck gently against a soft rubber pad

  3. the vibrating tuning fork should be held horizontally over the open end of the tube

  4. the prongs of vibrating tuning fork should not touch the tube

Show answer
Correct Option: A
Explanation:

The length of the air column inside the resonance tube is determined by the amount of water kept in the tube. 
If a water filled tube is inclined, the length of resonance column would be different at different lines parallel to the tube, and thus a number of resonating lengths would be created.

In ,a resonance tube the first resonance occurs at 16 cm and the second resonance occurs at 49 cm. The end corrections will be :

physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

  1. 0.3 cm

  2. 0.5 cm

  3. 0.8 cm

  4. 1.0 cm

Show answer
Correct Option: B
Explanation:

Answer is B.

The end correction is given as follows.
End corrections $\displaystyle =\frac { { l } _{ 2 }-3{ l } _{ 1 } }{ 2 }$
$\displaystyle =\frac { 49cm-3\times 16cm }{ 2 } =0.5cm$.
Hence, the end corrections will be 0.5 cm.