Sound

The characteristic sound of any instrument is referred to as the quality of that sound. "A form of energy, produced by rapidly vibrating objects, that can be heard by the human ear is called sound."

1.0Introduction

From our earliest years, we become accustomed to a great variety of sounds: our mother's voice, a telephone ringing, a kitten purring, a piano being played, a siren, a jet engine roaring, a rifle shot. Some of these sounds are pleasant to the ear and some are not. Sounds are a form of energy produced by rapidly vibrating objects. We hear sounds because this energy stimulates the auditory nerve in the human ear. In the 18th century, philosophers and scientists debated the question, "If a tree falls in the forest and no one is there to hear it, will there be sound ?" "Of course there will be," said the scientists, "because the crash of the tree is a vibrating source that sends out sound waves through the ground and the air." To them, sound was the motion of the particles in a medium caused by a vibrating object. "Of course not," said the philosophers, "because no observer is present." To them, sound was a personal sensation that existed only in the mind of the observer. This debate could never be resolved because one group was defining sound objectively in terms of its cause, and the other was defining it subjectively in terms of its effects on the human ear and brain. In physics, we study the transmission of sound objectively, leaving the subjective interpretation of the effects of sound on the human ear and brain to the philosophers.

Sound plays an important role in our life. It helps us to communicate with one another. We hear a variety of sounds in our surroundings. In the music room of your school you hear the sounds made by musical instruments like flute, tabla, harmonium, etc. (see figure)

2.0Sound Produced By A Vibrating Body

We can describe the sound which we hear in many ways. For example, lions roar, babies cry, birds chirp, corks pop, etc. All these types of sounds originate from vibrating objects. But, some vibrations are visible some are not. If you pluck a guitar string (see figure) or strike a low-frequency tuning fork (see figure), you can see the actual vibrations of the object. Similarly, if you watch the low-frequency woofer of a loudspeaker system, you can see it vibrating.

There are many vibrations that are not visible, however. When you speak, for instance, parts of your throat vibrate. When you make a whistling sound by blowing over an empty pop bottle, the air molecules in the bottle vibrate to produce sound.

A tuning fork is a two-pronged steel fork which produces sound when struck. A tuning fork makes a sound as the prongs of the fork vibrate in the air.

Jal Tarang

The Jal tarang is one of the most rarely heard instruments today. It is one of the oldest instrument in the world. It consists of china bowls filled with water and struck by means of two cane sticks.

Earlier, since china clay bowls weren't available, artists used to play this instrument with metal bowls. Each bowl can be tuned to the desired frequency by varying the quantity of water in it. These bowls are placed in a semi - circular arrangement around the player and played. Ancient texts mention instruments similar to this. Indian and Greek texts described such instruments. The Jal tarang has a pleasant characteristic tone. The player can produce on it, classical Indian ragas and light melodies as well. (see figure)

An artist playing on Jal tarang Table to show some musical instruments and their vibrating parts

An Ektara consists of a single stretched string which produces sound when it is vibrated using a bow

Amplitude Of A Vibrating Particle

As a particle vibrates, it repeats the same motion in equal time intervals. The distance in either direction from the mean position (or rest position) to maximum displacement is called its amplitude. (see figure)

Q. Why do you hear the sound of a water fall?

Explanation: When water falls from a certain height in a water fall, the vibrating water droplets produce sound that travels through air. This sound is heard by us when it reaches our ears. Sound of a water fall is a natural sound. Other natural sounds include animal sounds, from the chirping of crickets to the vocalizations of mammals, the sound of rain falling on the ground or on water, a rushing river, waves lapping on a shoreline, thunder, the crack of large pieces of ice shearing from a glacier or iceberg, and the crackle of a forest fire. Water and wind sounds are often heard in combination in nature. When we pluck the string of an instrument, like the sitar, the sound that we hear is not only that of the string.

Q. What do you understand by the term vibration or oscillation? Give some examples of vibrations you see in your daily life.

Explanation: The vibration (or oscillation) of an object is a cycle or a motion that is repeated over and over with the same time interval each time. Some examples of vibrations or oscillations we see in our daily life are : (1) A child swinging on a swing. (2) A simple pendulum oscillating about its mean position. (3) An oscillating spring that supports a vehicle.

3.0Wave Motion

Consider what happens to the surface of a pond when you drop a pebble into the water. The disturbance created by the pebble generates water waves that travel away from the disturbance (see figure). If you examine the motion of a leaf floating near the disturbance, you would see that the leaf moves up and down and back and forth about its original position. However, the leaf does not undergo any net displacement from the motion of the waves. The leaf's motion indicates the motion of the particles in the water. The water molecules move locally, like the leaf does, but they do not travel across the pond. That is, the water wave moves from one place to another, but the water and hence the leaf itself is not carried away with it.

Ripple waves in a pond start with a disturbance at some point in the water. This disturbance causes water on the surface near that point to move, which in turn causes points farther away to move. In this way, the waves travel outwards in a circular pattern away from the original disturbance.

In this example, the water in the pond is the medium through which the disturbance travels. Particles in the medium in this case are water molecules which move in vertical circles as waves pass. Note that the medium does not actually travel with the waves. After the waves have passed, the water returns to its original position. Waves that require a material medium are called mechanical waves. Not all wave propagation requires a medium. Electromagnetic waves, such as visible light, radio waves, microwaves, and X rays, can also travel through a vacuum.

In sound waves, the vibrations of particles of the medium through which it travels are parallel to the direction of travel of the wave. Thus, we can say that sound waves are longitudinal waves.

4.0Sound's Medium for propagation

Waves of almost every kind require a material medium in which they travel. Sound waves, for example, cannot travel through outer space, because space is very nearly a vacuum. In order for sound waves to travel, they must have a medium such as air or water. This means sound requires a medium to travel in.

Some school laboratories have a demonstration where a bell rings inside a jar. The experimental setup is shown in figure. As the air is pumped out of the jar, the sound gradually disappears. When the air is returned to the jar, the sound returns. Thus, in order for sound to be transmitted, a medium must be present.

Speed Of Sound Depends On

1. Medium: Sound waves can travel through solids, liquids, and gases. Because waves consist of particle vibrations, the speed of a wave depends on how quickly one particle can transfer its motion to another particle. For example, solid particles respond more rapidly to a disturbance than gas particles do because the molecules of a solid are closer together than those of a gas. As a result, sound waves generally travel faster through solids than through gases.
2. Temperature of the medium: As temperature rises, the particles of a gas collide more frequently. Thus, in a gas, the disturbance can spread faster at higher temperatures than at lower temperatures. In liquids and solids, the particles are close enough together that the difference due to temperature changes is less noticeable.

Sound waves propagate in three dimensions

Sound waves travel away from a vibrating source in all three dimensions. When a musician plays a musical instrument in the middle of a room, the resulting sound can be heard throughout the room because the sound waves spread out in all directions.

5.0Echolocation

Dolphins, bats, whales and orca whales rely on the production and reflection of sound to navigate, communicate, and hunt in dark and murky waters. The location of an object using reflected sound is called echolocation. Both animals produce clicks, whistles, and other sounds that vary in intensity, frequency, and pattern. Lower frequency sounds ( $0.5-50\mathrm{kHz}$ ) probably function mainly for social communication, while higher frequencies ( $40-150\mathrm{kHz}$ ) are probably used for echolocation. Most bats use echolocation for navigation in the dark and for finding food. The bat can identify an object by the echo and can even tell the size, shape, and texture of a small insect. If the bat detects a prey, it will generally fly towards the source of the echo, continuously emitting high frequency pulses until it reaches its target and scoops the insect up into its wing membranes and then into its mouth.

6.0Sound Produced By Humans

In humans, the sound is produced by the voice box or the larynx. Put your fingers on the throat and find a hard bump that seems to move when you swallow. This part of the body is known as the voice box. It is at the upper end of the windpipe. Two vocal cords are stretched across the voice box or larynx in such a way that it leaves a narrow slit between them for the passage of air (see figure).

Voice Box In Humans

When the lungs force air through the slit, the vocal cords vibrate, producing sound. The sound is amplified and modified by the group of parts collectively called the resonators. They are the pharynx, mouth and nasal cavity. Muscles attached to the vocal cords can make the cords tight or loose. When the vocal cords are tight and thin, the type or quality of voice is different from that when they are loose and thick. Greater tension in the vocal cords and higher air pressure create vibrations at higher frequencies.

• Your vocal cords are two thin folds of muscle and elastic tissue that relax when you are not speaking. To speak, your muscles stretch your vocal cords. Rock singers usually over-tense their vocal cords, which creates a dramatic sound but can cause vocal injuries such as nodules (small growths on the vocal cords that must be surgically removed). Shorter, thinner vocal cords vibrate at higher frequencies than longer or thicker ones. This explains why children, whose vocal cords are still growing, have thinner voices than adults. Muscles in the throat can stretch the vocal cords tighter, letting people vary their frequency within a limited range. The vocal cords in men are about 20 mm long. In women these are about 5 mm shorter. Children have very short vocal cords. This is the reason why the voices of men, women and children are different.
  
  Production of sound by human

7.0The Human Ear

The human ear consists of three sections: the outer ear, the middle ear, and the inner ear (see figure). The outer ear consists of the external ear (pinna) and the auditory canal. The external ear is shaped to collect sounds, which then travel down the auditory canal to the eardrum (see figure). The audible hearing range of a healthy young adult is approximately 20 to $20,000\mathrm{Hz}$. The middle ear is separated from the outer ear by the eardrum, a very tough, tightly stretched membrane less than 0.1 mm thick. The eardrum is forced to vibrate by sound coming down the ear canal. The vibration of the eardrum has the same frequency as the source of the sound waves.

Attached to the inside of the eardrum are three small interlocking bones: the hammer (malleus), the anvil (incus) and the stirrup (stapes). These bones transmit the vibrations of the eardrum to the inner ear, mechanically magnifying the pressure variations by a factor of 18. The stirrup transmits the eardrum vibrations to the threshold of the inner ear at the oval window. The vibrations set up pressure waves in the fluid that fills the inner ear's cochlea. The cochlea is a snail-shaped organ approximately 3.0 cm long, divided into two equal sections by a partition for most of its length. Waves are transmitted down one side of the cochlea, around the end of the partition, and back almost to the point of origin. As these waves move, they cause approximately 23,000 microscopic hairs to vibrate. Each hair is connected to a cell that converts the mechanical motion of the hair into an electrical signal, which in turn is transmitted to the brain by the auditory nerve.

• The cavity containing the middle ear is filled with air and is connected to the mouth by the Eustachian tube. This tube is normally closed, but it opens during swallowing or yawning, equalizing the air pressure in the middle ear. If the Eustachian tube becomes blocked, because of a cold for example, pressure equalization cannot take place and the result is pressure in the middle ear, which can be quite painful and can affect hearing.

Q. Is it correct to say that in every case, without exception, any radio wave travels faster than any sound wave?

Explanation: Yes. This is because any radio wave is an electromagnetic wave like light, thus it travels with the speed of light. The speed of light or radio wave in air is about $3\times 10^8\mathrm{m}/\mathrm{s}$ and speed of sound is about $340\mathrm{m}/\mathrm{s}$ which is approximately one million time smaller than the speed of a radio wave.

8.0Frequency Of A Vibrating Body

The number of oscillations (or cycles) that are taking place per second is called the frequency ( $f$ ) of a vibrating body. The SI unit used to measure frequency is the hertz ( Hz ), named after Heinrich Hertz (1857-1894), a German scientist who first produced electromagnetic waves in the laboratory. Time period of a vibrating particle The time period ( T ) of a vibrating particle is the time taken to complete one cycle or oscillation. It is measured in seconds.

Frequency, $\mathrm{f}=\frac{1}{\text{ Time period }}=\frac{1}{\mathrm{T}}$ or $\mathrm{f}=\frac{1}{\mathrm{T}}$ or Time period, $\mathrm{T}=\frac{1}{\text{ frequency }}=\frac{1}{\mathrm{f}}$ or $\mathrm{T}=\frac{1}{\mathrm{f}}$ Also, Frequency $=\frac{\text{ No. of cycles }}{\text{ time taken }}$

• Units of time $1\min =60\mathrm{s}$ $1\mathrm{ms}=10^{-3}\mathrm{s}$
• Always take the frequency in Hz and if it is given in cycles then take it in rps (revolution per second). $1\mathrm{KHz}=10^3\mathrm{Hz}$ $1\mathrm{MHz}=10^6\mathrm{Hz}$

• Time should always be taken in seconds.

Q. A mass hung from a spring vibrates $15$ times in $12$ s. Calculate: (a) the frequency (b) the period of the vibration.

• Decode the problem First understand what is given : 15 times means 15 cycles in 12 seconds. Identify the formula $\mathrm{f}=\frac{1}{\mathrm{T}}/\mathrm{f}=\frac{\text{ No.of Cycles }}{\text{ timetaken }}$ Solution (a) Given, number of cycles $=15$ cycles; total time $=12\mathrm{s}$; frequency, $\mathrm{f}=$ ? Now, $\mathrm{f}=\frac{15}{12}=1.25$ cycles $/$ second $=1.25\mathbf{Hz}$ (b) Now, $\mathrm{T}=\frac{1}{\mathrm{f}}$ or $\mathrm{T}=\frac{1}{\mathrm{f}}=\frac{1}{1.2}=0.83\mathrm{s}$

Q. The frequency of a wave is $5.0\times 10^2\mathrm{Hz}$. Calculate the time period. Solution: Given, $\mathrm{f}=5.0\times 10^2\mathrm{Hz};\mathrm{T}=$ ? We know that, $\mathrm{T}=\frac{1}{\mathrm{f}}$ or $\mathrm{T}=\frac{1}{5\times 10^2}=0.002$

Q. Calculate the period in seconds of each of these motions (a) a pulse beats 25 times in 15 s (b) a fan motor turns at $1200\mathbf{rpm}$ (revolutions per minute) Solution: (a) Given, no. of cycles $=25$; time taken $=15\mathrm{s}$ $\mathrm{f}=\frac{\text{ No. of cycles }}{\text{ time taken }}=\frac{25}{15}=1.67\text{ cycles }/\text{ second }.$ We know that, $\text{ or }\mathrm{T}=\frac{1}{\mathrm{f}}\text{ or }=\frac{1}{1.6}=0.625\mathbf{s}$ (b) Given, no. of cycles $=1200$; time taken $=1\min =60\sec$. $\mathrm{f}=\frac{\text{ No.of cycles }}{\text{ timetaken }}=\frac{1200}{60}=20$ cycles $/$ second We know that, or $\mathrm{T}=\frac{1}{\mathrm{f}}$ or $\mathrm{T}=\frac{1}{20}=0.05\mathbf{s}$

9.0Audible And Inaudible Sounds

The ears of most young people respond to sound frequencies of between 20 Hz and $20,000\mathrm{Hz}$. The sounds of frequencies between 20 Hz and 20,000 Hz that can be detected by the human ear is called audible sounds. The sounds of frequencies less than about 20 Hz and those higher than $20,000\mathrm{Hz}$ cannot be detected by the human ear. Such sounds are called inaudible sounds.

• Frequencies of less than 20 Hz are called infrasonic sounds. Frequencies that are higher than $20,000\mathrm{Hz}$ are called ultrasonic sounds.
• Some animals can hear sounds of frequencies higher than $20,000\mathrm{Hz}$. Dogs have this ability. The police use high frequency whistles which dogs can hear but humans cannot.

Elephants use infrasonic sound waves to communicate with one another. Their large ears enable them to detect these low-frequency sound waves, which have relatively long wavelengths. Elephants can effectively communicate in this way, even when they are separated by many kilometers.

Q. A metallic blade fixed in a wall is made to vibrate at its free end. The vibrations of the blade gradually decrease and finally stop after some time. Why?

Explanation: The vibrations of the blade gradually decrease after some time due to the friction offered by the air resistance and they finally get stopped. (see figure)

10.0Characteristics Of Audible Sounds

1. Pitch: The frequency of an audible sound wave determines how high or low we perceive the sound to be, which is known as pitch. As the frequency of a sound wave increases, the pitch rises. The frequency of a wave is an objective quantity that can be measured, while pitch refers to how different frequencies are perceived by the human ear. In other words, the frequency determines the shrillness or pitch of a sound. If the frequency of vibration is lower, we say that the sound has a lower pitch [see figure (a)]. If the frequency of vibration is higher we say that the sound is shrill and has a higher pitch [see figure (b)].
   

• We can say that a thinner voice like a female voice has high pitch while a thicker (heavy) voice like a male voice has low pitch. Sounds of musical instruments like guitar, sitar, violin, veena are high pitch sounds while sounds of drum, tabla, dholak are low pitch sounds.
• If you have ever been near a pond on a summer evening, you might have heard the crickets chirping and the bullfrogs croaking. You could easily distinguish between the sounds because cricket sounds have a high pitch and bullfrog sounds have a low pitch. These sounds are different because their frequencies are different.

2. Loudness: The loudness of the sounds humans perceive relates to the intensity of the sound. Sound intensity is energy carried by the sound per unit time per unit area. Sound intensity is usually measured in watt/(meter) ${}^2$ or ( $\mathrm{W}/{\mathrm{m}}^2$ ). The loudness of a sound depends on the amplitude of vibration. The greater the amplitude, the higher the volume of the sound. A speaker making a loud sound moves back and forth more than a speaker making a soft sound. (see figure) Unit of loudness : The loudness is expressed in a unit called decibel (dB). On the decibel scale, 0 dB is called the threshold of hearing.
   
   
   Amplitude and loudness are related

Loudness of sound coming from various sources

Human ear is sensitive to the sound intensity (loudness) ranging from 0-180 dB.

3. Quality (or timbre): Quality of a sound is the property by which two sounds of the same pitch (or frequency) emitted by two different sources can be distinguished from each other. It depends on the waveform of the sound produced by a source. For example, a clarinet sounds different from a violin because of differences in quality (timbre), even when both instruments are sounding the same note at the same volume (see figure).

• The pitch of the musical note produced in a stringed instrument like guitar depends on the length, diameter, and tension of the string.
• If the string is shorter, narrower, or tighter, the pitch increases. For example, the thinner guitar strings produce a higher pitch than the thicker strings.

11.0Noise And Music

We hear different types of sounds around us. Some sounds are pleasing while some sounds cause discomfort to us. Suppose construction work is going on in your neighborhood. The sounds coming from the construction site are not pleasing. Similarly, we do not enjoy the sounds produced by horns of buses and trucks. Such unpleasant sounds are called noise. In a classroom, if all the students speak together, the sound produced will be a noise. Noise originates from a source where the frequencies are constantly changing in a random manner. Displayed on an oscilloscope, noise does not have a constant waveform [see figure (a)].

On the other hand you enjoy sounds from musical instruments. Musical sound is one which is pleasing to the ear. Sound produced by a harmonium is a musical sound. The string of a sitar also gives out a musical sound. A musical note originates from a source vibrating in a uniform manner with one or more constant frequencies. Music is the combination of musical notes. With an oscilloscope, music is displayed as a constant waveform [see figure (b)].

• If a musical sound becomes too loud, it will not remain melodious. It will become unpleasant and thus, it will sound like a noise.

12.0Noise Pollution

'Noise' is a by-product of industrialisation and modern civilisation. It is the state of undesirable loud sounds of different kinds producing in the atmosphere due to the various modern civilisation activities like running of vehicles, industrial processes, loud speakers, etc.

Presence of excessive or unwanted sounds in the environment is called noise pollution.

1. Sources of noise pollution

• Industrialisation : Industrialisation is the major source of noise pollution. Industries use machinery that makes loud and irritating sounds of various kinds which produce the noise pollution.
• Transportation : Another major cause of noise pollution particularly in cities is transportation such as buses, trucks, cars, scooters, etc. that creates noise pollution because of their engines and horns.
• Electrical devices at home : At home, the major cause of noise pollution is the use of electrical devices like mixer-grinder, cooler, fan, television, tape-recorder, radio, vacuum cleaner, etc.
• Social functions: Loud speakers and musical bands used in the social functions also cause the noise pollution to some extent in cities.

2. Effects of noise pollution

• Impairment of hearing (deafness) due to the prolonged exposure to loud noise.
• Severe damage to ear drum due to a sudden loud noise.
• Lack of sleep
• Hypertension (high blood pressure)
• Anxiety
• Noise pollution may also cause damage to heart, brain, liver and can result in emotional disturbances.

3. Measures to limit noise pollution

The following factors should be kept in view for controlling noise pollution:

Source of noise pollution

• Setting industries away from crowded areas.
• Using better designed engines.
• Lubricating and maintaining machines.
• Enforcing laws to get rid of noise producing vehicles and to restrict the use of loud speakers and amplifiers. Even at home, television and music systems should be run at low volumes.
• Use of automobile horns should be minimised.

Path of noise

• Planting of trees along the roads. Interrupting the path of sound by materials which absorb the sound. Acoustic materials wool and mufflers (silencer) can be used.

Receptive organs: Using ear mufflers or cotton plugs.

13.0Hearing Impairment

The total hearing impairment is rare, and it is usually from birth itself. Partial disability is generally the result of a disease, injury or age. Children with impaired hearing need special care. By learning sign language, such children can communicate effectively. Because speech develops as the direct result of hearing, a child with a hearing loss may have defective speech also.

14.0Hearing Aid

A hearing aid is an electronic device that amplifies sounds for people with hearing impairments. Hearing aids have the same basic components as any home entertainment system, except all the components are miniaturised and the amplified sound is delivered directly to the ear. The microphone, amplifier, miniature receiver (speaker), and battery are enclosed in a shell, which is worn behind or within the ear. A small tube directs the amplified sound from the receiver into the ear canal.

15.0Mind Map

16.0Some Basic Terms

• Accustomed - Familiar with something.
• Stimulates - To make something more active.
• Succession - A number of things that follow each other in time or order.
• Chirping - Repeated short, high pitched sounds by bird.
• Miniaturised - On a very small scale, reduce in size.
• Perception - Ability to hear.
• Oscilloscope - Device which is used to display oscillations or vibrations.
• Interrupting - Break the continuity of an activity.
• Excessive - More than is necessary.
• Hops - Moving by jumping on one foot.
• Tone - Musical sound with reference to its pitch, quality.

17.0Solved Examples On Sound

• If 100 oscillations are produced in 1 min , then find the frequency? Solution: Given; Number of cycles = 100 ; time taken $=1\min .=60\sec$. $\mathrm{f}=\frac{\text{ No. of cycles }}{\text{ time taken }}=\frac{100}{60}$ $=\frac{10}{6}$ cycles $/$ second or Hz .
• If a tuning fork vibrates in a manner such that it makes 625 vibrations in 25 seconds then find the frequency of sound. Solution: Given; Number of vibrations $=625$; time taken $=25\sec$. $\mathrm{f}=\frac{\text{ No. of vibrations }}{\text{ time taken }}=\frac{625}{25}=25\mathbf{Hz}$.
• Determine the frequency of a guitar string that oscillates with a period of 0.004 seconds. Solution: Given; $\mathrm{T}=0.004\sec$. $\therefore \mathrm{f}=\frac{1}{\mathrm{T}};\mathrm{f}=\frac{1}{0.004}=\frac{1000}{4}=250\mathbf{Hz}$
• A dragon fly beats its wings with the frequency of 75 Hz . What is the periods of the wings? Solution: Given; f = 75 Hz $T=\frac{1}{f}=\frac{1}{75}=0.013\mathbf{sec}$
• A red capped manakin is a bird that can flap its wings faster than a humming bird at 5400 beats per minute. What is the period of its flapping wings? Solution: $$\begin{gathered} \mathrm{F}=\frac{\text{ Number of vibration }}{\text{ Timetaken }} \\ =\frac{5400}{60}=90\mathrm{Hz} \end{gathered}$$ $$\begin{gathered} \mathrm{T}=\frac{1}{\mathrm{f}}=\frac{1}{90} \\ =0.011\mathbf{sec}. \end{gathered}$$
• A dog, happy to see its owner wags its tails 2.50 times a second. (a) What is the period of the dogs wagging tail? (b) How many wags of its tail will the dog make in 1 minute. Solution: Given; $\mathrm{f}=2.5\mathrm{Hz}$ (a) $T=\frac{1}{f}=\frac{1}{2.5}=0.4\mathbf{sec}$. (b) Number wags of its tail in one minute, frequency $=$ number of wags $\times$ time number of wags $=2.5\times 60=150\text{ wags }$
• Observe the graph, find out the amplitude of the wave. Solution:
  
  Since, amplitude is the maximum displacement of particale from its mean position. Therefore, it is 2 m from the graph.
• Find out the amplitude of the travelling wave shown below.
  
  Solution: The peak to peak value of the wave is 0.32 m . And, amplitude is half of the peak to peak value. $\therefore$ amplitude $=\frac{0.32}{2}=0.16\mathbf{m}$.
• Draw the amplitude time graph of the wave of amplitude 4 cm and frequency 5 Hz. Solution:
  
  Given: $\mathrm{f}=5\mathrm{Hz}$ $\mathrm{T}=\frac{1}{\mathrm{f}}=\frac{1}{5}=0.2\mathbf{sec}$.
• Wave motion of a body is shown in figure.
  
  What with be the amplitude of a vibrating body? Solution: Since, amplitude is the maximum displacement from the mean position. Therefore, amplitude $=\frac{40}{2}=20\mathbf{m}$.