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Introduction to sound waves - class-VIII

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The speed of a supersonic wave, as compared to that of sound is

  1. $less$

  2. $more$

  3. $equal$

  4. $1/10$


Correct Option: B
Explanation:

Prefix in the word "Supersonic" is 'super', means superior to sound waves. Supersonic waves are faster than the sound wave in air.
Option "B" is correct.

The frequency of a man's voice is $300\space Hz$. If the velocity of sound waves is $336\space ms^{-1}$, the wavelength of the sound is

  1. $1.12\space m$

  2. $300\times336\space m$

  3. $330/336\space m$

  4. None of these


Correct Option: A
Explanation:

We are given, frequency $f=300 Hz$, and velocity $v=336 ms^{-1}$,

From the relation $v=f \times \lambda$,

$\lambda = v/f =336/300=1.12 m$

Option "A" is correct.

 769Hz longitudinal wave in air has a speed of 344m/s. At a particular instant, what is the phase difference (in degrees) between two points 5.0 cm apart?

  1. 30

  2. 40

  3. 45

  4. 60


Correct Option: B
Explanation:

Given that,

The frequency of wave is $\nu = 769 Hz$

The speed of wave is $v = 344 ms^{-1}$

The wavelength of wave is given by

$\lambda = \dfrac{v}{\nu}$

$\lambda = \dfrac{344}{769}$

$\lambda = 0.447 m = 44.7 cm$

Hence, the phase difference between two points 5.0 cm apart is

$\dfrac{5}{44.7} \times 360^\circ = 0.1118 \times 360^\circ = 40.24^\circ \approx40^\circ$

A rod $70\space cm$ long is clamped from middle. The velocity of sound in the material of the rod is $3500\space ms^{-1}$. The frequency of fundamental note produced by it is :

  1. $3500\space Hz$

  2. $2500\space Hz$

  3. $1250\space Hz$

  4. $700\space Hz$


Correct Option: B
Explanation:

SInce rod is clamped at middle, therefore only nodes can form at that point, and at free end only antinode can form, therefore for fundamental mode of frequency,

$\lambda/4=L/2$

$\lambda=2L=2\times 70 cm=1.4 m$

$v=3500\  ms^{-1}$ is given, 

We know, $v=f \times \lambda$ or $f = \dfrac{v}{\lambda}=3500/1.4=2500 Hz$

Option "B" is correct.

A sonometer wire, $100\ \text{cm}$ in length has a fundamental frequency of $330\ \text{Hz}$. The velocity of propagation of transverse waves along this wire is :

  1. $330\ \text{ms}^{-1}$

  2. $660\ \text{ms}^{-1}$

  3. $115\ \text{ms}^{-1}$

  4. $990\ \text{ms}^{-1}$


Correct Option: B
Explanation:

For the fundamental frequency $(f _0=330 Hz),\ \lambda=2 L=200\ \text{cm} = 2\ \text{m}$


then from the formula, $v=f _0 \times \lambda= 330 \times 2.0= 660 \text{ms}^{-1}$

If the frequency of a sound wave is increased by 25%, then the change in its wavelength will be

  1. 25% decrease

  2. 20% decrease

  3. 20% increase

  4. 25% increase


Correct Option: B
Explanation:
The frequency  of wave is given by

$\nu = \dfrac{v}{\lambda}$

$\lambda = \dfrac{v}{\nu}$

When the frequency of a sound wave is increased by 25%, then the new 
wavelength is

$\lambda' = \dfrac{v}{\nu+\dfrac{25}{100}\nu}$

$\lambda' = \dfrac{v}{\nu+\dfrac{1}{4}\nu}$

$\lambda' = \dfrac{v}{\dfrac{5}{4}\nu}$

$\lambda' = \dfrac{4v}{5\nu}$

Hence, the percent change in wavelength is

$\dfrac{\lambda - \lambda'}{\lambda} \times 100 = \dfrac{\dfrac{v}{\nu} - \dfrac{4v}{5\nu}}{\dfrac{v}{\nu}} \times 100$

$\Rightarrow -\dfrac{1}{4} \times 100 = -20$%.

Hence, wavelength decreases by 20%

Sound waves of wavelength $\lambda $ travelling with velocity $v$ in a medium enter into another medium in which their velocity is $4v$. The wavelength in $2^{nd}$ medium is :

  1. $4\lambda$

  2. $\lambda $

  3. $\lambda/4 $

  4. $ 16\lambda $


Correct Option: A
Explanation:

From $v=n\lambda $ we find $\lambda\propto v$ because frequency n is constant .

Therefore ,
new wavelength = $4\lambda $

A $40\ cm$ long brass rod is dropped, one end first on to a hard floor but it is caught before it topples over. With an oscilloscope it is determined that the impact produces a $3\ kHz$ tone. The speed of sound in brass is:

  1. $1200\ m/s$

  2. $2400\ m/s$

  3. $3600\ m/s$

  4. $3000\ m/s$


Correct Option: B
Explanation:

Both ends are free and therefore antinodes are formed.
The relation between the wavelength of the wave and the length of the rod for fundamental frequency will be:

$\Rightarrow l=\dfrac{\lambda}{2} \ \ \Rightarrow \lambda=2l$

The speed of the wave in the rod is:
$v=f\lambda = 2\times 40\times 3\times 10^{3}$$=2400\ ms^{-1}$

The frequency of a man's voice is 300 Hz and its wavelength is 1 meter. If the wavelength of a child's voice is 1.5 m, then the frequency of the child's voice is :

  1. 200 Hz

  2. 150 Hz

  3. 100 Hz

  4. 350 Hz.


Correct Option: A
Explanation:

$\nu _1\lambda _1= \nu _1\lambda _1$ since $v= \nu\lambda$ is same for both a man and child.

$ \therefore 300 \times 1 =  \nu _2 \times  1.5$


$ \Rightarrow \nu _2 = 200 : Hz$

The wave produced in a resonance tube is

  1. Longitudinal

  2. Transverse

  3. Transverse stationary

  4. Longitudinal stationary


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. 

Two sound waves of wavelengths $1\space m$ and $1.01\space m$ produce $10$ beats in $3$ seconds. Then, the velocity of the sound is

  1. $330\space ms^{-1}$

  2. $333.3\space ms^{-1}$

  3. $336.7\space ms^{-1}$

  4. none of the above


Correct Option: C
Explanation:

From the formula, $v=f \lambda$

and the velocity of the sound in air is frequency independent.

for two frequencies $f _1$ and $f _2$, wavelengths are $\lambda _1$ 

and $\lambda _2$ , then the beats will be

$f _1-f _2=v\left(\dfrac{1}{\lambda _1}-\dfrac{1}{\lambda _2}\right)=v\left(\dfrac{\lambda _2-\lambda _1}{\lambda _2  \lambda _1}\right)$

$\dfrac{10}{3}=v\left(\dfrac{0.01}{1.0\times 1.01}\right)$

$v=\dfrac{10\times 1.0\times 1.01}{3.0\times 0.01}=336.66\ \text{ms}^{-1}$

Option "C" is correct.

Sound waves cannot pass through

  1. a solid-liquid mixture

  2. an ideal gas

  3. a liquid-gas mixture

  4. a pefect vacuum


Correct Option: D
Explanation:

Sound cannot travel through a perfect vacuum. A vacuum is an area without any air, like space. So sound cannot travel through space because there is no matter for the vibration to work in.

Sound waves in air are _________ waves.

  1. longitudinal

  2. radio

  3. transverse

  4. electromagnetic


Correct Option: A
Explanation:

Sound waves in air and any fluid medium are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound waves moves.

A _________________ wave has oscillations in the same direction as its motion.

  1. Longitudinal

  2. Oscillatory

  3. Vibrational

  4. matter


Correct Option: A
Explanation:

A longitudinal wave has oscillations in the same direction as its motion.
Longitudinal waves, also known as l-waves, are waves in which the displacement of the medium is in the same direction as the direction of travel of the wave. Longitudinal waves are also called compressional waves or compression waves, because they produce compression and rarefaction when traveling through a medium.  In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave. 

The sound propagates in a gaseous medium as :

  1. transverse waves

  2. longitudinal waves

  3. both (a) and (b)

  4. neither (a) nor (b)


Correct Option: B
Explanation:

Sound is a sequence of waves of pressure which propagates through compressible media such as air or water. Sound propagates as longitudinal waves in gaseous medium. Longitudinal waves are the waves in which the displacement of the medium is in the same direction, or the opposite direction to the direction to the direction of propagation of wave.

Match the columns

i) particles of medium move parallel to the propagation of disturbance. a) Transverse wars
ii) particles of medium oscillate up and down about their mean position. b) longitudual wars.
iii) particles of the medium oscillate oscillate back and forth about their position of vest.
iv) particles move about their mean positions in a direction perpendicular to the direction of waves propagation
  1. a - i, ii, b - iii, iv

  2. a - i, iii, b - ii, iv

  3. a - iii, iv, b - i, ii

  4. a - iv, ii, b - i, iii


Correct Option: D
Explanation:

In a wave if the particles of medium , vibrate perpendicular to the direction of wave motion (disturbance) then this wave is called a longitudinal wave .

 If the particles of medium , vibrate parallel to the direction of wave motion (disturbance) then this wave is called a transverse wave .
According to these definitions , we can match the given columns as :
a-iv ,ii and b-i,iii . 

Sound waves are transverse mechanical waves. State whether true or false.

  1. True

  2. False


Correct Option: B
Explanation:

Sound waves are longitudinal mechanical waves.

Sound waves are

  1. Transverse waves

  2. Longitudinal waves

  3. Ultrasonic waves

  4. Stationary waves


Correct Option: B
Explanation:

Particles of the sound waves vibrate in the direction of wave. So it is characterized under longitudinal waves.

Fix up one end of a slinky to a hook and hold it horizontally. Vibrate the other end to and fro along the length of the spring. If you look the spring carefully , you will see some parts of the spring are pushed closer , while some other parts are pulled apart.

  1. The portions which are pushed closer are called compressions

  2. The portions which are pulled apart are called rarefactions

  3. Both A and B are correct

  4. Neither of A and B is correct


Correct Option: C
Explanation:

Compressions are the regions of high density and rarefactions are regions of low density.These compressions and rarefactions result because sound is able to reflect off fixed ends and interfere with incident waves vibrates longitudinally; the longitudinal movement of air produces pressure fluctuations. 

Which of the following are true.

  1. the sound and light waves both are longitudinal waves

  2. both the sound and light waves are transverse

  3. in air ,the sound waves are longitudinal as well as transverse

  4. in air, the sound waves are longitudinal and the light waves are transverse


Correct Option: D
Explanation:

Longitudinal waves are always characterized by particle motion being parallel to wave motion. A sound wave travelling through air is a classic example of a longitudinal wave. Transverse wave moves perpendicular to the direction of wave motion. Light waves are transverse in nature.

The waves in which the particles of the medium vibrate in a direction perpendicular to the direction of wave motion is known as:

  1. transverse wave

  2. propagated waves

  3. longitudinal waves

  4. stationary waves


Correct Option: A
Explanation:

The waves in which the particles of the medium vibrate in a direction perpendicular to the direction of wave motion is known as transverse wave. Examples of these waves are: vibrations in strings, ripples on water surface and electromagnetic waves.

Compressions and rarefactions are seen in

  1. longitudinal and transverse waves

  2. longitudinal waves only

  3. transverse waves only

  4. none


Correct Option: B
Explanation:

   Longitudinal waves propagate in a medium in the form of compressions and rarefactions . When pressure becomes high , medium particles come closer and a compression is formed and due to low pressure , rarefaction is formed .

  Transverse waves propagate in the form of crests and troughs .

Sound is called longitudinal wave because

  1. sound need a material medium for propagation

  2. the molecules of the medium oscillate to and fro about their mean position in the direction of propagation

  3. sound waves moves in the direction of its production

  4. all reasons are correct


Correct Option: B
Explanation:

When a sound travels through their medium, the molecules in the air oscillate to and fro about their mean positions in the direction of propagation of sound wave.

Compressions and rarefactions are seen in :

  1. longitudinal and transverse waves

  2. longitudinal waves only

  3. transverse waves only

  4. none of these


Correct Option: B
Explanation:

In case of longitudinal waves compressions and rarefactions are seen. Compressions are the regions of high density and rarefactions are regions of low density.In transverse waves generally crest and troughs are seen.

When vibrating string moves in reverse direction then

  1. it lowers pressure to right

  2. it lowers pressure to left

  3. it lowers pressure to center

  4. it increases pressure to right


Correct Option: A
Explanation:

When vibrating string moves in a reverse direction, the pressure due to the vibrant molecules lowers to right.

When sound travels through air, the air particles :

  1. vibrate along the direction of wave propagation

  2. vibrate but not in any fixed direction

  3. vibrate perpendicular to the direction of wave propagation

  4. do not vibrate


Correct Option: A
Explanation:

Sound is a longitudinal wave.  If the particles of a medium vibrate or oscillate to and fro about their equilibrium position along the direction of propagation of disturbance then the wave is called longitudinal wave.

How does sound from a sound producing body travel through air to reach our ears?

  1. through crest and troughs

  2. through compression and rarefaction

  3. both

  4. none


Correct Option: B
Explanation:

Sound from a sound producing body travel through air to reach our ears by making regular compression and rarefaction.

How longitudinal waves are different from other waves?

  1. Particles of medium move in a direction parallel to direction of energy transport

  2. Particles of medium move in a direction perpendicular to direction of energy transport

  3. Particles of medium move in a direction below to direction of energy transport

  4. None


Correct Option: A
Explanation:

Longitudinal waves are different from the others waves because in longitudinal waves particles of medium move in a direction parallel to direction of energy transport for longitudinal waves.

In a graphical presentation of longitudinal waves as attached, the peak of wave is called

  1. Compression

  2. Rarefaction

  3. Reflection

  4. Refraction


Correct Option: A
Explanation:

Graphical representation of longitudinal waves is the variation of pressure (y-axis) with the distance (x-axis). We know that, the pressure is higher at the point where the element of medium is compressed and the pressure is low where the element of medium is rarefied.
So, the wave forms a pressure peak at compression and pressure valley at rarefaction.

Sound is a good example of

  1. Transverse Waves

  2. Longitudinal Waves

  3. Both

  4. None


Correct Option: B
Explanation:

Sound waves are longitudinal waves which require a material medium (solid, liquid or gas) to propagate. So, sound waves cannot pass through a perfect vacuum.

Which of the following is true?

  1. The sound and light waves both are longitudinal waves

  2. Both the sound and light waves are transverse

  3. In air ,the sound waves are longitudinal as well as transverse

  4. In air, the sound waves are longitudinal and the light waves are transverse


Correct Option: D
Explanation:

If the particles of a medium vibrate or oscillate to and fro about their equilibrium position along the direction of propagation of disturbance then the wave is called longitudinal wave.

In the graphical presentation as attached, what does the valley of wave known as

  1. Compression

  2. Rarefaction

  3. Reflection

  4. Deflection


Correct Option: B
Explanation:

Graphical representation of longitudinal waves is the variation of pressure (y-axis) with the distance (x-axis). We know that, the pressure is higher at the point where the element of medium is compressed and the pressure is low where the element of medium is rarefied.
So, the wave forms a pressure peak at compression and pressure valley at rarefaction.

Which of the following is NOT a characteristic of longitudinal wave?

  1. Wavelength

  2. Amplitude

  3. Velocity

  4. None


Correct Option: D
Explanation:

All of the above are characteristics of Longitudinal waves

The sound propagates in a gaseous medium by

  1. Transverse waves

  2. Longitudinal waves

  3. Both (a) and (b)

  4. None of these


Correct Option: B
Explanation:

For transverse wave, cohesion is an important property in the medium through which the wave energy can be transported. Gas does not have such a cohesion property. Hence there is no chance for transverse waves to be propagated through gas medium. So the sound propagates in a gaseous medium by longitudinal wave.

Fill in the blank. 

Sound waves in air are __________waves.

  1. Longitudinal

  2. Radial

  3. Transverse

  4. Electromagnetic


Correct Option: A
Explanation:

Longitudinal waves are waves in which the motion of the individual particles of the medium is in a direction that is parallel to the direction of energy transport. Sound waves in air (and any fluid medium) are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves.

Sound does not exhibit the property of

  1. Reflection

  2. Doppler Effect

  3. Diffraction

  4. Polarization


Correct Option: D
Explanation:

Polarization is exhibited only by Transverse waves. Sound waves being longitudinal do not exhibit this phenomenon. 

A uniform tub to length $60.5\,cm$ is held vertically with its lower end dipped in water. A sound source of frequency $500\,Hz$ sends sound waves into the tube. When it is $50\,cm$, the tube resonates with the source of sound. Two lowest frequencies (in Hz), to which tube will resonate when it is taken out of water, are (approximately)

  1. $281, 562$

  2. $281, 843$

  3. $276, 522$

  4. $272, 544$


Correct Option: C

If wind blows in a direction opposite to the sound propagation, then the velocity of the sound

  1. increases

  2. decreases

  3. remains constant

  4. Cannot be determined


Correct Option: B

A replica of longitudinal waves can be best observed 

  1. by swinging a pendulum

  2. by pressing and releasing a horizontal spring

  3. by striking a guitar string

  4. by rotating a top


Correct Option: B
Explanation:

If we press and release a horizontal spring, it exhibits a confined motion of compression and rarefaction. So, it shows a replica of longitudinal waves. A swinging pendulum performs simple harmonic motion. A struck guitar string exhibits a replica of transverse waves. A rotating top exhibits rotational motion.

Sound waves in air are

  1. transverse

  2. longitudinal

  3. electromagnetic

  4. polarised


Correct Option: B
Explanation:

Sound waves are longitudinal waves because the disturbance of the medium particles is parallel to the direction of propagation of wave. The compression and rarefraction pulses produced moves in the direction parallel to the propagation direction of wave.

A tuning fork is excited by striking it with a padded hammer. What would be the nature of the vibrations executed by the prongs as well as the stem of the fork respectively ? (The reference direction is that of the propagation of the sound wave.)

  1. Both vibrate longitudinally

  2. Both vibrate transversely

  3. The prong vibrate longitudinally whereas the stem vibrates transversely

  4. The prong vibrate transversely whereas the stem vibrates longitudinally


Correct Option: C

The ratio of the velocity of body and velocity of sound is known as

  1. laplace number

  2. positive number

  3. stable number

  4. mach number


Correct Option: D
Explanation:

Definition of Mach Number is $Ma=\frac{V _{body}}{V _{\mbox{sound in that medium}}}$.
Option "D" is correct.

Sound wave are not polarized because:

  1. Their speed is less

  2. A medium is needed for their propagation

  3. These are longitudinal

  4. Their speed depends on temperature


Correct Option: A
Explanation:
   Sound wave are not polarized because,their speed is less.So the option is A.

The ratio of the speed of a body to the speed of sound is called:

  1. Mach number

  2. Doppler Ratio

  3. Sonic index

  4. Refractive index


Correct Option: A
Explanation:

Mach number of a body is the ratio of its speed to that of local sound.
The local speed of sound, and thereby the Mach number, depends on the condition of the surrounding medium, in particular the temperature and pressure. The Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. 

Which type of wave is produced in the stem of tuning fork?

  1. transverse

  2. transverse stationary

  3. longitudinal

  4. longitudinal stationary


Correct Option: C
Explanation:

When tuning fork is sounded by striking its one end on rubber pad then the prongs vibrate in and out and stem vibrate up and down. Hence, vibration of prongs are transverse and those of stem are longitudinal. 

Which of the following is the longitudinal wave?

  1. Sound waves

  2. Waves on plucked string

  3. Water waves

  4. Light waves


Correct Option: A
Explanation:

In sound waves vibration of particle is along the propagation of wave So it is longitudinal and in other options all are transverse wave as vibration of particle is perpendicular to the propagation of wave.  

Consider the following statement:
(a) Sound waves are longitudinal in nature.
(b) Sound waves cannot travel through vacuum.
(c) Sound waves are produced by oscillating charged particles only.
(d) Sound waves are electromagnetic waves.
Which of the following statements are correct ?

  1. (a) and (b)

  2. (b) and (c)

  3. (a), (b) and (d)

  4. (a),(b),(c) and (d)


Correct Option: A
Explanation:

Sound waves are longitudinal waves. It needs a medium to propagate. Sound waves are example of mechanical waves, not electromagnetic waves. Electromagnetic waves are created by the vibration of an electric charge.

A longitudinal waves consists of

  1. crest and troughs in the medium

  2. compressions and rarefactions in the medium

  3. crest and troughs in vacuum 

  4. Both A and B


Correct Option: B
Explanation:

Longitudinal waves, also known as l-waves, are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel of the wave. Longitudinal waves are also called compression waves or compression waves, because they produce compression and rarefaction when traveling through a medium.  In longitudinal waves, the displacement of the particle's is parallel to the propagation of the wave. 

In case of longitudinal waves, the particles of medium vibrate

  1. in the direction of wave propagation

  2. opposite to the direction of wave propagation

  3. at right angles to the direction of wave propagation

  4. none of the above


Correct Option: A
Explanation:

Longitudinal waves, also known as l-waves, are waves in which the displacement of the medium is in the same direction as the direction of travel of the wave. Longitudinal waves are also called compressional waves or compression waves, because they produce compression and rarefaction when traveling through a medium.

Longitudinal waves are also called

  1. Rarefactional waves

  2. Compressional waves

  3. Sound waves

  4. Light waves


Correct Option: B
Explanation:

Sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. If a sound wave is moving from left to right through air, then particles of air will be displaced both rightward and leftward as the energy of the sound wave passes through it. The motion of the particles is parallel to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.
Longitudinal waves, also known as l-waves, are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of travel of the wave. Longitudinal waves are also called compressional waves or compression waves, because they produce compression and rarefaction when traveling through a medium.  In longitudinal waves, the displacement of the medium is parallel to the propagation of the wave.

769Hz longitudinal wave in air has a speed of 344m/s. How much time is required for the phase to change by 90 degrees at a given point in space? 

  1. 0.325 ms

  2. 3.25 ms

  3. 32.5 ms

  4. 325 ms


Correct Option: A
Explanation:

Given that, 

The frequency of wave is $\nu = 769 Hz$.

The speed of wave is $v = 344 ms^{-1}$.

We know, the frequency of a wave is the number of oscillations per 
unit time. The period (T) of a wave is the time that it takes for one complete oscillation, i.e., to change its phase through $360^\circ$.
Hence,

$T = \dfrac{1}{\nu}$

$T = \dfrac{1}{769}$

$T = 0.0013 s$

$T = 1.3 ms$

Here, the phase change is 90 degrees at a given point in space.  

$\dfrac{90}{360} = \dfrac{1}{4}$

Hence, the time period required to complete one fourth oscillation is

$T = \dfrac{1.3}{4} = 0.325 ms$

The musical note A is a sound wave. The note has a frequency of 440 Hz and a wavelength of 0.784 m. Calculate the speed of the musical note in m/s.

  1. 343

  2. 345

  3. 34

  4. 346


Correct Option: B
Explanation:

Let,

The frequency of the musical note is $\nu = 440 Hz = 440 s^{-1}$

The wavelength of the musical note is $\lambda = 0.784 m $

Now, the frequency of the musical note is 

$\nu = \dfrac{v}{\lambda}$

where, v is the speed of the musical note 

Hence, the speed of the musical note is

$v = \nu \lambda$

$v = 440 \times 0.784$

$v = 344.96 \approx 345 ms^{-1}$

The type of waves that can be propagated in solids are :

  1. Longitudinal

  2. Transverse

  3. both

  4. None


Correct Option: C
Explanation:

Mechanical waves (longitudinal waves and transverse waves) are waves which propagate through a material medium (solid, liquid or gas) at a wave speed which depends on the elastic and inertial properties of that medium. 
The transverse waves depends on the rigidity of the medium hence, can propagate through solid and liquid medium but not through gases.
The longitudinal waves depends on resistance to compression or volume elasticity of the medium hence, can propagate through solid, liquid and gases.

The frequency of a tuning fork is 384 Hz and velocity of sound in air is $\displaystyle 352 ms^{-1}$. How far sound has travelled when fork completes 36 vibration?

  1. 33 m

  2. 16.5 m

  3. 11 m

  4. 22 m


Correct Option: A
Explanation:

$\displaystyle x = v.t = v \times \dfrac{no \ of \ complete \ vibration }{frequency \ of fork}=325$ x $\displaystyle\frac{36}{384} = 33 m$

What is the ratio of the speed of sound in neon and water vapor at the same temperature. It is nearest to :

  1. 2.5

  2. 2

  3. 1.5

  4. 1


Correct Option: D
Explanation:

According to the Avogadro's law , at same temperature and pressure the number of molecules of different gasses are equal. Therefore density will not change in either case of neon or water vapor. And the speed of sound waves is a function of density and temperature. So in this case doesn't matter.
Option "D" is correct. 

The ratio $(v)$ of velocities of sound in dry air and humid air is

  1. $v<1$

  2. $v>1$

  3. $v=1$

  4. Zero


Correct Option: A
Explanation:

Because water molecules have less mass than the average air molecules $(N _2 (28 \text{amu}),$ while water $H _2O (18 amu)).$ But It will happen if and only if the pressure is unchanged. Given that dry and humid air are both under the same pressure then we have smaller density for humid air.
And velocity of sound waves$,v,$ in a medium is given by,


$v=\sqrt{\dfrac{\gamma E}{d}}$, here $\gamma = \dfrac{C _P}{C _V}$, 

$E$ is elasticity of the medium, and $d$ is the density.

Since, density of air decreases with humidity increases. therefore velocity of sound increases in humid air.
Option "A" is correct.

A rope length $\displaystyle l$ and mass $\displaystyle m$ hanges freely from the ceiling. The velocity of transverse wave as a function of position $\displaystyle x$ along the rope is proportional to

  1. 1 / $\displaystyle \sqrt x$

  2. $\displaystyle \sqrt x$

  3. $\displaystyle x$

  4. $\displaystyle x^0$


Correct Option: B
Explanation:

$\text{Mass per unit length of rope} =\dfrac{m}{l}$
Mass of rope of length $x =\dfrac { m }{ l } x$
Tension, $T = \dfrac { m }{ l } xg$
Velocity, $v=\sqrt { \dfrac { T }{ m }  } =\sqrt { \dfrac { mgl }{ lm } x }$ 
     which is directly proportional to $\sqrt { x } $

When the stem of a vibrating tuning fork is pressed a sounding board, then

  1. transverse vibrations are communicated through stem to the board.

  2. longitudinal vibrations are communicated through stem to the board

  3. both longitudinal and transverse vibrations are communicated through stem on the board

  4. none of the above


Correct Option: B
Explanation:

When the tuning fork is set into vibration, the stem of tuning fork vibrate  up and down with longitudinal vibrations hence, when the stem of a vibrating tuning fork is pressed a sounding board, then longitudinal vibrations are communicated through stem to the board.

When slinky is stretched out in a horizontal direction and first coils are vibrated horizontally then which waves are generated?

  1. Longitudinal Waves

  2. Transverse Waves

  3. Surface waves 

  4. None


Correct Option: A
Explanation:

Longitudinal Waves are generated when slinky is stretched out in a horizontal direction and first coils are vibrated horizontally 

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