CBSE Class 8 Science Sound Solved Examples

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Class 8 Science – Sound: Solved Examples and Exercises

Solved examples

Figure shows the mean position A and the extreme positions B and C of the bob of an oscillating pendulum. Identify which of the following distances represent a quarter oscillation and which represent half an oscillation: (a) BA (b) AC (c) BAC (d) CAB (e) AB (f) ABA

Answer: BAC + CAB is a complete oscillation, so each of BAC and CAB is half an oscillation. BA, AC and AB are each half of BAC, so these three are quarter oscillations. ABA = AB + BA; as AB = BA = a quarter oscillation, ABA is a half oscillation.
So: quarter oscillation: (a) BA, (b) AC, (e) AB; half oscillation: (c) BAC, (d) CAB, (f) ABA.

The frequency of a source of sound is 100 Hz. How many times does it vibrate in a minute?

Answer: Here the frequency is 100 Hz, and 1 minute = 60 seconds. The number of vibrations = 100 × 60 = 6000.

The figure shows the displacement of a particle with distance in a periodic wave moving along a string. (a) Find the wavelength. (b) If the wave travels at a speed of 10 cm/s, find the time period and the frequency of the wave.

Answer:

(a) From the figure, the distance between consecutive crests is 1 cm. Hence, the wavelength is 1 cm.

(b) Using \( \lambda = vT \):

\[ T=\frac{\lambda}{v}=\frac{1\ \text{cm}}{10\ \text{cm/s}}=0.1\ \text{s} \]

The frequency is

\[ \nu=\frac1T=\frac{1}{0.1\ \text{s}}=10\ \text{Hz} \]

A sound wave has a frequency of 1,000 Hz and a wavelength of 34 cm. How long will it take to travel 1 km?

Answer:

Here \( \nu = 1000\ \text{Hz} \) and \( \lambda = 34\ \text{cm} = \frac{34}{100}\ \text{m} \). The wave speed is

\[ v=\nu\lambda=(1000\ \text{s}^{-1})\left(\frac{34}{100}\ \text{m}\right)=340\ \text{m/s} \]

The time taken to travel 1 km is

\[ t=\frac{x}{v}=\frac{1000\ \text{m}}{340\ \text{m/s}}=2.94\ \text{s} \]

An oil tanker explodes at sea. At that instant an aircraft and a submarine were present vertically above and below the oil tanker respectively, at equal distances from it. Find the ratio of the times taken by the sound waves to reach them. (Speed of sound in air = 340 m/s, speed of sound in sea water = 1,520 m/s.)

Answer:

Let the aircraft and the submarine be x m above and below the tanker respectively. The time taken by the sound to reach the aircraft is \( t_{air}=\frac{x}{340}\ \text{s} \), and to reach the submarine is \( t_{water}=\frac{x}{1520}\ \text{s} \). So

\[ \frac{t_{air}}{t_{water}}=\frac{x/340}{x/1520}=\frac{1520}{340}=4.47 \]

A person clapped his hands near a cliff and heard the echo after 5 s. What is the distance of the cliff from the person if the speed of sound, v, is taken as 346 m/s?

Answer: The distance travelled by the sound = v × t = 346 m/s × 5 s = 1730 m. In 5 s the sound has to travel twice the distance between the cliff and the person (to the cliff and back). Hence, the distance between the cliff and the person = 1730 m ÷ 2 = 865 m.

Basic level assignment

What is sound and how is it produced?

Answer: Sound is a form of energy which produces the sensation of hearing in our ears. It is produced by vibrating objects, such as a plucked string, a struck drum or the vocal cords.

Why is a sound wave called a mechanical wave?

Answer: A sound wave needs a material medium (solid, liquid or gas) to travel. It is carried by the vibration of the particles of the medium, and it cannot travel through a vacuum. Such waves are called mechanical waves.

How does the sound produced by a vibrating object in a medium reach your ear?

Answer: The vibrating object pushes and pulls the particles of the medium next to it, which makes regions of high pressure (compressions) and low pressure (rarefactions). These travel through the medium as a wave, from particle to particle, until they reach the eardrum in our ear and make it vibrate.

Give two practical applications of reflection of sound waves.

Answer: (i) Echo ranging (SONAR) is used to find the depth of the sea and to locate the objects under water. (ii) Megaphones, horns and the curved sound boards in concert halls use the reflection of sound to send the sound in a particular direction. (A stethoscope also works on the reflection of sound.)

Distinguish between periodic motion and oscillatory motion. Is the motion of an electric fan periodic or oscillatory?

Answer: A periodic motion is a motion which repeats itself after equal intervals of time, e.g. the motion of the Earth around the Sun. An oscillatory motion is a to-and-fro motion about a mean position, e.g. the motion of a pendulum. Every oscillatory motion is periodic, but every periodic motion is not oscillatory. The motion of an electric fan is periodic (it rotates and repeats), but it is not oscillatory, as it is not to and fro about a mean position.

What do you understand by the equilibrium position of a pendulum?

Answer: It is the position at which the pendulum bob rests when it is not disturbed (the mean position, the lowest point of its path). The net force on the bob is zero there.

Explain with a diagram what you understand by a complete oscillation.

When the bob starts from the mean position A, goes to one extreme B, comes back through A to the other extreme C and returns to A, it has completed one oscillation: A → B → A → C → A.

When a wave propagates in a medium, what is transferred from one place to another, matter or energy?

Answer: Energy. The particles of the medium only vibrate about their mean positions; they do not move along with the wave.

Give three examples of transverse waves.

Answer: Waves on a stretched string, ripples on the surface of water, and light waves (electromagnetic waves).

A longitudinal wave travels from east to west in air. In which direction do the particles of air move?

Answer: In a longitudinal wave, the particles vibrate along the direction of travel of the wave, so the particles of air move to and fro along the east–west line.

A sitar player plucks the wire of a sitar to a side and releases it. After a short time, each part of the wire starts vibrating in a direction perpendicular to the wire. Is the propagation of this disturbance a longitudinal or a transverse wave?

Answer: It is a transverse wave, because the particles of the wire vibrate perpendicular to the direction in which the disturbance travels (along the wire).

A long spring is fixed at one end. A person holding the other end compresses the spring with a jerk. The compression travels along the length of the spring. Is it an example of a longitudinal wave or a transverse wave?

Answer: It is a longitudinal wave, because the coils of the spring move to and fro along the length of the spring, which is the direction of travel of the compression.

Is a sound wave longitudinal or transverse?

Answer: A sound wave in air (and in liquids) is a longitudinal wave.

Name two quantities that vary periodically at a place in air as a sound wave travels through it.

Answer: The pressure and the density of the air (the displacement of the air particles also varies periodically).

In which of the three media – air, water or steel – does sound travel the fastest?

Answer: In steel.

Which has the larger frequency – infrasonic sound or ultrasonic sound?

Answer: Ultrasonic sound (more than 20,000 Hz), while infrasonic sound has a frequency below 20 Hz.

What is reverberation? How can it be reduced?

Answer: Reverberation is the persistence of sound in a big hall after the source has stopped, because of the repeated reflections of the sound from the walls, roof and floor. It can be reduced by covering the walls and ceilings with sound-absorbing materials such as curtains, carpets, acoustic tiles and cushioned seats.

What is the loudness of sound? On what factors does it depend?

Answer: Loudness is the sensation of how strong or weak a sound is. It depends on the amplitude of the vibration (the larger the amplitude, the louder the sound), on the distance from the source, and on the sensitivity of the listener's ear. It is measured in decibels (dB).

Explain how bats use ultrasound to catch their prey.

Answer: A bat produces ultrasonic squeaks while it flies. The waves are reflected by the prey (such as an insect) and come back to the bat as an echo. From the time taken and the direction of the echo, the bat finds the position of the prey and catches it.

How is ultrasound used for cleaning?

Answer: The object to be cleaned is placed in a cleaning solution, and ultrasonic waves are sent through it. The strong vibrations remove the dust, grease and dirt from the parts of the object, even from the hard-to-reach places (such as the spiral tubes and electronic parts).

Explain how defects in a metal block can be detected using ultrasound.

Answer: Ultrasonic waves are sent through one side of the metal block. If there is a crack or a hole inside, the waves are reflected from it and do not pass through. The detector on the other side receives less (or no) signal, or receives the reflected echo, which shows the presence and the position of the defect.

Explain how the human ear works.

Answer: The outer ear (pinna) collects the sound and sends it through the ear canal to the eardrum, which starts vibrating. The three small bones of the middle ear (the hammer, anvil and stirrup) amplify the vibrations and pass them to the inner ear. In the cochlea, the vibrations become electrical signals, which the auditory nerve carries to the brain, and we hear the sound.

Choose the correct option(s) in the following

If a wave completes 20 vibrations in 2.5 s, its frequency is

1. 20 Hz
2. 8 Hz
3. 200 Hz
4. 50 Hz

Answer: (B) 8 Hz. Frequency = 20 ÷ 2.5 = 8 Hz.

An observer standing at the sea coast observes 54 waves reaching the coast per minute. If the wavelength of the wave is 10 m, the velocity of the wave will be

1. 4.5 m/s
2. 9 m/s
3. 18 m/s
4. 27 m/s

Answer: (B) 9 m/s. Frequency = 54 ÷ 60 = 0.9 Hz, so v = fλ = 0.9 × 10 = 9 m/s.

Sound waves cannot pass through

1. a solid–liquid mixture
2. an ideal gas
3. a liquid–gas mixture
4. a perfect vacuum

Answer: (D) a perfect vacuum, since sound needs a medium.

If five waves are produced in one second, the time period of one wave is

1. 0.20 s
2. 0.25 s
3. 0.10 s
4. 0.05 s

Answer: (A) 0.20 s. T = 1 ÷ 5 = 0.2 s.

The distance between two successive rarefactions is called

1. frequency
2. wavelength
3. wave velocity
4. amplitude

Answer: (B) wavelength.