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

In a resonace air column experiment, first and second resonance are obtained at length of air columns $l _{1}$ and $l _{2}$ the third resonance will be obtained at a length of

  1. $2l _{2}-l _{1}$
  2. $l _{2}-2l _{1}$
  3. $l _{2}-l _{1}$
  4. $3l _{2}-l _{1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a resonance tube, the resonance lengths are l1 = lambda/4, l2 = 3*lambda/4, and l3 = 5*lambda/4. The difference between consecutive resonances is lambda/2. Thus, l3 = l2 + (l2 - l1) = 2*l2 - l1.

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

Two pendulums of length $1.21m$ and $1.0m$ start vibrating. At some instant, the two are in the mean position in same phase. After how many vibrations of the longer pendulum, the two will be in phase?

  1. $10$
  2. $11$
  3. $20$
  4. $21$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The time period of a pendulum is T = 2*pi*sqrt(L/g). T1/T2 = sqrt(L1/L2) = sqrt(1.21/1.0) = 1.1 = 11/10. For them to be in phase, n1*T1 = n2*T2. n1/n2 = T2/T1 = 10/11. After 11 vibrations of the longer pendulum (T1), the shorter one (T2) will have completed 10 vibrations.

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

A sound wave of wavelength $\lambda$ travels towards the right horizontally with a velocity $V$. It strikes and reflects from a vertical plane surface, traveling at a speed $v$ towards the left. The number of positive crests striking in a time interval of $3s$ on the wall is:

  1. $3(V+v)/ \lambda$
  2. $3(V-v)/ \lambda$
  3. $(V+v)/3\lambda$
  4. $(V-v)/3\lambda$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative velocity of the wave crests with respect to the wall is (V + v). The distance covered in time t is (V + v) * t. The number of crests is distance / wavelength = (V + v) * t / lambda. For t = 3s, this is 3(V + v) / lambda.

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

A person observes a change of 2.5% in frequency of sound of horn of a car . If the car is apporaching forward the person  sound velocity is 320 m/s then velocity of car in m/ s wil be appromately

  1. 8

  2. 800

  3. 7

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Doppler formula n'$=\dfrac{nv}{v-v _s}$ $n' > n$
if $n2100\quad n'=102.5$
Since source is moving towards distance so
$102.5=\dfrac{100\times 320}{320-v _s}$
$\therefore v _s=8$m/sec.
Multiple choice physics stationary waves determining wavelength and speed of sound resonance tube resonance and sonometer

In an experimental determination of the velocity of sound using a Kundt's tube, standing waves are set up in the metallic rod as well as in the rigid tube containing air, both the waves have the same :

  1. amplitude

  2. frequency

  3. wavelength

  4. particle velocity
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed, wavelength and amplitude change as it is traveling through different material on the other side frequency must remain constant to conserve energy (which is dependent solely on frequency).

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

In Kundt's tube experiment wavelength in the metallic rod and air are 80 cm and 16 cm respectively. If the velocity of sound in air is $\displaystyle 300   ms^{-1}$ then the velocity of sound in rod will be

  1. $\displaystyle 80 ms^{-1}$
  2. $\displaystyle 3.75 ms^{-1}$
  3. $\displaystyle 240 ms^{-1}$
  4. $\displaystyle 1500 ms^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Velocity of sound in air $V _{air}=300 ms^{-1}$, and $\lambda _{air}=16 cm=0.16 m$.

let us say velocity of sound in metal pipe $V _{metal} ms^{-1}$, and 

$\lambda _{metal}=80 cm=0.8 m$.

frequency remain unchanged when medium changes,

 $V _{metal}=\frac{\lambda _{metal}}{\lambda _{air}} V _{air} ms^{-1}=(0.8/0.16)*300 ms^{-1}=1500 ms^{-1}$.

Option "D" is correct.

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

  1. $204$ $cm/sec$
  2. $280$ $cm/sec$
  3. $58$ $cm/sec$
  4. $80$ $cm/sec$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

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

  1. Length of air column

  2. Diameter of air column

  3. Both A and B

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 .

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

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

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

Sound is a mechanical wave requiring a medium, so its speed depends on the medium's properties like temperature and density. Light is an electromagnetic wave that can travel through a vacuum, and its speed is a fundamental constant independent of the medium's temperature.

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

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

  1. resonance tube

  2. kundt's tube

  3. sonometer.

  4. organ pipe
Reveal answer Fill a bubble to check yourself
B Correct answer
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.