Tag: stationary waves

Questions Related to stationary waves

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:

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

  1. $3(V+v)/ \lambda$

  2. $3(V-v)/ \lambda$

  3. $(V+v)/3\lambda$

  4. $(V-v)/3\lambda$

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Correct Option: A

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

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

  1. 8

  2. 800

  3. 7

  4. 6

Show answer
Correct Option: A
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.

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 :

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

  1. amplitude

  2. frequency

  3. wavelength

  4. particle velocity

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Correct Option: B
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).

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

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

  1. $\displaystyle 80 ms^{-1}$

  2. $\displaystyle 3.75 ms^{-1}$

  3. $\displaystyle 240 ms^{-1}$

  4. $\displaystyle 1500 ms^{-1}$

Show answer
Correct Option: D
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.

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.  

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. $512\ Hz$

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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 $=4\times 128$
$= 512\ Hz$

A wire of density $\rho $ is stretched between the clamps at a distance $L$ apart while being subjected to an extension $\ell (<<L)$, Y is Young's modulus of the wire. The lowest resonant frequency of transverse vibration of the wire is approximately given by :

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

  1. $f= \dfrac{1}{2L}\sqrt{\dfrac{YL}{\ell\rho }}$

  2. $f= \dfrac{1}{2L}\sqrt{\dfrac{Y\rho L}{\ell^2 }}$

  3. $f= \dfrac{1}{2L}\sqrt{\dfrac{Y\ell}{L\rho }}$

  4. $f= \dfrac{1}{2L}\sqrt{\dfrac{L\rho}{Y\ell }}$

Show answer
Correct Option: C
Explanation:
$Y=\dfrac{Stress}{Strain}=\dfrac{TL}{A\ell}$

$T= \dfrac{YA\ell}{L}$

mass per unit length

$f= \dfrac{1}{2L}\sqrt{T/m} $

$\ m\Rightarrow mass\:  per \: unit\:  length$

$f= \dfrac{1}{2L}\sqrt{\dfrac{Y\ell}{L\rho }}$

The wave produced in a resonance tube is

physics stationary waves sound as a wave of disturbance vibrations in a tuning fork vibrations in tuning fork

  1. Longitudinal

  2. Transverse

  3. Transverse stationary

  4. Longitudinal stationary

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Correct Option: D
Explanation:

Waves produced in a resonance tube are sound waves. Two sound waves in opposite direction interfere with each other to create resonance. As sound waves are longitudinal waves, waves produced are longitudinal stationary.