Waves: Important Questions

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Very Short Answer Questions [1 mark]

Ques: Why does the velocity of sound increase on a cloudy day?

Ans: The velocity of sound increases on a cloudy day because on a cloudy day, the air is wet, also it contains a lot of moisture and the air density is also low. Hence, velocity is known to be inversely proportional to density, velocity increases.

Ques: Of what nature are ultrasonic waves and what is their frequency?

Ans: Ultrasonic waves are longitudinal in nature and they have frequencies greater than 20 kHz.

Ques: Suppose, a tuning fork produces resonance in a closed organ pipe. But the same tuning fork which produced resonance in a closed organ pipe is unable to produce resonance in an open organ pipe of equal length. Why?

Ans: The tuning fork is unable to produce resonance because the fundamental frequencies of both open and closed organ pipes of equal length are known to be different.

Ques: Why echoes are not heard in a small room?

Ans: Echoes are not heard in a small room because of the minimum distance between the obstacle reflecting sound waves and the source of sound is comparatively less than 17m in a small room.

Ques: What are the two properties that are common to all types of mechanical waves?

Ans: The two properties that are common to all types of mechanical waves are:

1. For their propagation, they require a material medium.
2. The material medium itself does not move with the wave.

Ques: When one places his/her ear at the end of a long steel pipe, he/she can hear two sounds at the same time when a workman hammers the other end of the pipe. Why?

Ans: He/she can hear two sounds because the sound is transmitted through both air and medium.

Ques: In a perfectly rigid rod, what will be the velocity of sound and why?

Ans: Ina perfectly rigid rod, the velocity of sound will be infinite. It is because the value of Young’s modulus of elasticity is infinite for a perfectly rigid rod.

Ques: Why a stationary wave is so named?

Ans: A stationary wave is so named because there is no any net propagation of energy in this wave.

Ques: One can make waves in a pond by throwing a stone in it. What will be the source of energy producing the wave?

Ans: The kinetic energy of the stone thrown in a pond is the source of energy of the wave.

Ques: What is the most basic property of the wave?

Ans: Frequency is known to be the most basic property of the wave.

Also check: Potential Energy

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Short Answer Questions [2 marks]

Ques: State the limitations of Doppler’s effect.

Ans: Doppler’s effect is applicable only when there is any relative velocity between the source and the listener and also it should be less than the velocity of sound. The effect will not be applicable if the relative velocity present is greater than the velocity of sound.

Ques: Explain why frequency is the most fundamental property of a wave?

Ans: When a wave passes from one medium to another, its velocity and wavelength changes but the frequency remains the same. Hence, frequency is considered the most fundamental property of a wave.

Ques: Suppose, one starts filling an empty bucket with water, the pitch of sound that is produced goes on changing. Why?

Ans: An empty bucket always behaves as a closed organ pipe. So, when the bucket starts filling with water, the length (l) of the resonating air column decreases, and hence frequency increases. Since the pitch of sound depends upon the frequency, it changes when there is a change in frequency.

Ques: Why is the sound that is produced in the air not heard by a person deep inside the water?

Ans: The velocity of sound in water is much less than the velocity of sound in air. So, the sound waves are mostly reflected from the surface of the water without going any deep. Only a little amount of refraction of sound from air to water takes place. Moreover, the refracted sound waves from the air die off after travelling a short distance in the water. Therefore, no sound waves can reach deep inside the water.

Ques: Explain why transverse elastic waves can’t propagate through a fluid?

Ans: When a transverse elastic wave travels through a solid, a shearing strain is developed which is supported by the elastic solid because of the development of a restoring force. Thus, elastic waves can propagate through a solid.

But in the case of liquid or gas (i.e. fluid), they can’t support a shearing strain. So, without that, there will be no any restoring forces when there are transverse displacements. Thus, elastic waves can’t propagate through a fluid.

Ques: Doppler’s effect on sound is said to be asymmetric. Explain.

Ans: Sound waves always require a material medium for their propagation.

The apparent frequency is said to be different whether the source moves towards the stationary observer or an observer moves towards the stationary source. Thus, Doppler’s effect on sound is said to be asymmetric.

Ques: Sound is produced by vibratory motion, explain why then a vibrating pendulum does not produce sound?

Ans: The sound which we can hear has a frequency ranging from 20 Hz to 20,000 Hz.

The frequency of a vibrating pendulum does not lie within the audible range and hence it does not produce sound.

Also check: Semiconductor Diode

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Long Answer Questions [3 Marks]

Ques: Which physical quantity is said to be represented by the ratio of the intensity of wave and energy density? Why?

Ans: Velocity is the physical quantity which is represented by the ratio of the intensity of wave and energy density.

We know that, intensity  = energyarea ×time

And energy density = energyvolume

Therefore, intensity energy density = energyarea ×time ÷ energyvolume

= energy ×volumearea ×time ×energy

= area ×length area ×time

= lengthtime

= distancetime

= velocity

Ques: How far does the sound travel in the air when a tuning fork of frequency 280Hz makes 15 vibrations? The value of the velocity of sound is given 336 ms^-1.

Ans: Given,

Velocity of sound, v = 336ms^-1

Frequency, f = 280Hz

Therefore, time of one complete vibration,

T=1f

=1280S

Time to complete 15 vibrations,

t=15T

=15 ×1280

Let x be the distance covered in time (t), then we get:

x=v ×t

=336 ×15280

=18m

Therefore, x = 18m

Ques: What is the intensity level in dB of sound whose intensity is 10^-6 watt m-2. Take the value of zero levels of intensity = 10^-2 watt m^-2.

Ans: Given,

I = 10^-6 watt m^-2

I₀= 10^-12 watt m^-2

L =?

Now,

L=log10 II0=log10 10^-610^-12

= log10 10⁶

=6 log10 10 = 6 ×1 = 6B

As 1B = 10 dB

Therefore, L = 6 ×10 = 60 dB

=60 dB

Therefore, the intensity level of sound whose intensity is 10^-6 watt m^-2 is 60 dB.

Ques: What are the basic conditions required for the formation of stationary waves?

Ans: The basic conditions that are required for the formation of stationary waves are as follows:

1. Both, direct and reflected waves must be travelling along the same line.
2. For the formation of stationary waves, the superposing waves should be either longitudinal or transverse.
3. For the formation of stationary waves, there should not be any relative motion between the medium and oppositely travelling waves.
4. The period and amplitude of the superposing waves should be the same.

Also check: Wheatstone Bridge

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Very Long Answer Questions [5 Marks]

Ques: Suppose, a drop of water that is 2 mm in diameter is falling from a height of 50 cm in a bucket generates a sound that can be heard from a distance of 5 m. Taking every gravitational energy difference equal to sound energy, the transformation being spread in time is over 0.2s. Find out the average intensity of the sound. Take g = 10 ms².

Ans: Given,

P of water = 10³ kg m^-3

D = 2 mm

Therefore, radius = r = 22 = 1 mm = 10^-3 m

H = 50cm = 0.50 m

g = 10 ms^-2

d = 5m

t = 0.2 s

Therefore, a = area in which the sound is heard

=4πd²

I = Intensity of sound =?

Now,

I =energy transferencetime ×area

=P.E.of droptime × area

=mght × a ….. (1)

Now,

mgh =43πr³ p gh

a =4πd²

=4×π×52 …… (2)

Therefore, from the above equation (1) and (2), we get:

I = 43π ×(10^-3)3×10³ ×10×0.50.2 ×4π (5)²

= 43 ×(10^-9×10³ ×10×0.52 × 25 ×4

=13×10^-6

=10³×10^-7

=3.33 ×10^-7 w m^-2

Therefore, the average intensity of sound, (I) is 3.33 ×10^-7 w m^-2 .

Ques: What are the different characteristics of wave motion?

Ans: The different characteristics of wave motion are as follows:

1. Wave motion is defined as a form of disturbance that travels in a medium due to repeated periodic motion of the particles of the medium.
2. The wave velocity is not the same as the particle velocity.
3. The vibrating particles of the medium possess both kinetic and potential energy.
4. The particle velocity is different at different positions of its vibrations whereas the wave velocity is constant throughout any given medium.
5. Waves can undergo reflection, refraction, diffraction, dispersion, and also interference.

Ques: A pipe that is 20 cm long is seen to be closed at one end. Which vibration mode of the pipe is resonantly excited by a given source of 430 Hz? If both ends of the pipe are open, will the same source be in resonance with the pipe? (Speed of sound in air is given 340 m₅^-1)

Ans: Given,

Length of the pipe, l = 20 cm = 0.2 cm

Source frequency = n the normal mode of frequency, u_n = 430 Hz

Speed of sound, u = 340 m s

Now,

In a closed pipe, the normal mode of frequency, u_n is given by the relation:

U_n =2n-1 u4 ;n is an integer 

= 0, 1, 23….

430 = 2n-13404 ×0.2

2n – 1 = 430 × 4 × 0.2340

2n – 1 = 1.01

2n = 2.01

n = 1

Therefore, the first harmonic mode of the pipe is resonantly excited by the given source.

In a pipe whose both ends are open, the nth mode of vibration frequency is given by the relation shown below:

u_n = Nu2l

u_n = 2 V Au

= 2 ×0.2 ×430340

=0.5

Since the number of the mode of vibration (n) has to be an integer but the value is 0.5. Hence, we can conclude that the given source does not produce any resonant vibration in an open pipe.

Ques: State the differences between:

1. Transverse and Longitudinal waves
2. Progressive and stationary waves

Ans: a: The differences between transverse and longitudinal waves are mentioned below as follows:

Transverse waves:

1. Waves in which the motion of the particles is perpendicular to the motion of the wave as a whole are known as transverse waves.
2. They can travel in the form of alternate troughs and crests.
3. These waves can be formed in solids and on the surface of liquids only.
4. These waves can be polarised.

Longitudinal waves:

1. Waves that can cause the particles in a medium to vibrate parallel to the direction of the wave motion are known as longitudinal waves.
2. They can travel in the form of alternate compressions and rarefaction.
3. These waves can be formed in any medium, be it solid, liquid, or gas.
4. These waves can’t be polarised.

b: The differences between progressive and stationary waves are mentioned below as follows:

Progressive waves:

1. Waves that travel continuously in a medium without any change in their direction and amplitude are known as Progressive waves.
2. Energy is transported in the medium.
3. No any particle of the medium is permanently at rest.
4. There is no change in density and pressure at all points of the medium.

Stationary waves:

1. The combination of two waves moving in opposite directions, each wave having the same amplitude and frequency are known as stationary waves.
2. No energy is transported in the medium.
3. The particles of the medium at nodes are only at rest.
4. The changes of pressure and density are maximum at nodes and minimum at antinodes.

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