Physics

Chapter - 7: Waves and Sound

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Simple Harmonic Motion

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What is simple harmonic motion?

The harmonic motion of constant amplitude in which the acceleration is proportional and oppositely directed to the displacement of the body from a position of equilibrium is called the simple harmonic motion.

Why the vibrating motion of tuning fork is called oscillatory motion?

We know, if a vibratory body moves in one direction on the first half of its period and moves in the opposite direction during the remaining time then the motion of the body is called oscillatory motion. During vibration, the tuning fork moves in one direction in the first half of its period and moves in the opposite direction during the remaining time. And so the motion of tuning fork is oscillatory.

The motion of swing is an oscillatory motion?

If a vibrating body moves in one direction on the first half of its period and moves in the opposite direction during the remaining time then the motion of the body is called oscillatory motion. The swing moves in one direction in the first half of its period and moves in one opposite direction during the remaining time then the motion of the body is called oscillatory motion. And so the motion of the swing is oscillatory.

The motion of the wave of water in the pond is periodic?

When waves are formed in water it displays not only transitional motion but also moves in a upward and downward direction. In other words, the water particles gain periodic motion. Crests and troughs are formed simultaneously in the water, which propagates as a transverse wave. Thus, waves in pond water are periodic motion.

Wave

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What is wave?

The disturbance or variation that transfers energy progressively from point to point in a medium is called a wave. The medium through which the wave travels may experience some local oscillations as the wave passes, but the particles in the medium do not travel with the wave.

What is mechanical wave?

Mechanical wave is the wave that requires a medium to transport their energy from one location to another. The sound wave is an example fo a mechanical wave.

Characteristics of Waves

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• For mechanical wave a medium is necessary. Waves can be created in water, a wave can be transmitted in a spring, a wave can be created in a rope. The sound we hear is also a wave and its medium is air.

• When a wave propagates through a medium, the particles of the medium oscillate (vibrate or go up-down) about it own position but are not displaced permanently with the wave.

• Energy can be transferred from one place to another through waves. The more the energy, the more the amplitude  of the wave. 

• Every wave has a velocity; this velocity depends on the nature of the medium. In air, the velocity of sound is 330 m/s, in water this velocity is 1439 m/s. The velocity of a wave in a tight rope (under tension) will be more than the velocity of the wave in a loose rope.

• Reflection or refraction occurs for waves. At the time of travelling from one medium to another medium, if part of a wave returns back to the first medium to the second medium, it is reflection. If we hear external sound when we are submerged under water it is due to refraction.

• Among all the characteristics of waves, the most important is superposition, even though this is not observed often by our eyes in our daily lives. Let us consider that two different places reach one place. When one wave is trying to pull the medium up, another wave is then trying to pull it down. These are the subjects of superposition, which will give you a deep insight into waves, and you will be able to be understand it very clearly. Two waves, can reinforce one another or can destroy each other.

Types of Wave

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There are two types of wave. They are -

a) Longitudinal wave

b) Transverse wave

a) Longitudinal wave: When a wave propagates through a medium, the direction of vibration and the direction of the velocity of wave is the same, this type of wave is called longitudinal wave. Example of longitudinal wave sound wave, spring wave, etc.

b) Transverse wave: When a wave propagates through a medium, the direction of vibration is perpendicular to the direction of the velocity of the wave, this type of wave is called transverse wave. Example of transverse wave is water wave.

Wave related quantities

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What is the frequency?

Frequency is the number of cycles per second in a wave.

What is the period?

The period is the time taken for one complete cycle of vibration to pass a given point.

What is the amplitude?

Amplitude is the maximum height of the wave in any direction from the equilibrium position.

What is phase?

Phase is a particular point in time on the cycle of the waveform, measured as an angle in degrees.

What do you understand by the phase of a wave?

The phase is an important characteristics of any wave. Phase specifies the location of a point within a wave cycle of a repetitive waveform. It might represent the direction of velocity, displacement, velocity or acceleration at any instance. In a transverse wave, the crests and the troughs are always in the same phase.

Sound Wave

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To produce sound waves a source is needed, a medium to send it through, and any type of receiver to receive that sound.

There are many sources of sound around us.

How to produce sound

The voice of males is deep and that of the females is high pitched - Explain.

The most familiar source is our throat; sound is created by the vibration of the vocal cord when air flows through it in our throat. We will feel the vibration if we tough our throat during conversation. 

The voice of a male is deep and the voice of female and children is sharp. When we make a sound then air comes out through throat from our lungs. In our throat there is a wind pipe through which air enters the lungs and come out from the lungs. 

To produce sound larynx is situated upon it. There are two membranes which work as valves, called vocal cords. These vibrate during the flow of air and produce sound.

The vocal cords of males become stiff with the increasing of age, whereas for females it remains soft. This is why males produce sound of low frequency and females produce sound of high frequency. Due to this, the voice of males is deep and that of the females is high pitched.

Sound can be produced by vibrating the thin diaphragm.

If we hit a school bell, it starts vibrating and sound is produced. If we grip the bell then the vibration will stop and the sound will stop instantly. After producing sound by vibration, we need a medium to transmit it from one place to another. 

Sound can also be sent through liquids and solids but we are used to hearing sound using air as a medium. 

How does the sound wave circulate through air?

Sound wave is a longitudinal wave. Because of the contraction and expansion of air layer the sound moves forward. The sound spreads in the form of longitudinal wave. This sound wave makes a sense of hearing in our ear by being circulated in air medium.

Sound wave is which type of wave?

Sound wave is a longitudinal wave.

What is hearing range?

The hearing range describes the range of frequencies that can be heard by humans or other animals. The range of human hearing is 20 Hz to 20,000 Hz.

What is the audibility range?

The range of the frequency of sound that we can hear is called the range of audibility.

Explain that sound and the contraction and expansion of air layer is complementary to one another.

To circulate medium is needed for sound. The sound circulates through the medium by contraction and expansion of air layer. This way sound moves forward. That's why it can be said that sound and contraction and rarefaction are complementary to one another.

Characteristics of Sound Wave

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Sound is a mechanical wave, because sound wave is produced due to the vibration of a body, and for its transmission an elastic medium is needed. This is a longitudinal wave, because the direction of propagation of the wave and the direction of vibration is the same. The velocity of sound depends on the property of the medium. In gaseous mediums its velocity depends on the temperature and humidity of the medium. The intensity of sound is proportional to the square of the amplitude of the wave. Therefore, if the amplitude of a wave is high, the intensity of the sound will be high and if the amplitude is low, the intensity will be low.

Why some sounds are harmonic while others are noise?

When the vibration is periodic the sounds are harmonic. When many waves superpose on one another they appear to be melodious. For example, harmonium, flute, guitar, etc. On the other hand, when symmetry is absent between the sound waves generated then the sound appears to be noisy, annoying and harsh. For example, chaos in Bazar, the sound of moving vehicles, etc.

Echo

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Since sound is one type of wave, it can have reflection. If someone speaks in a big empty building it creates a reverberating sound. This is due to reflection. Within the building the distance is not enough to hear the sound separately. When we hear something the feeling persist for around 0.1 s, so to hear two sounds separately, it needs separation of 0.1 s differences between two sounds. Velocity of sound is 330 m/s, therefore to create a difference of 0.1 s, sound has to travel at least 33 m.

If we stand in front of a big wal, a building, or a high hill at least half of this distance (16.5 m), the sound will take 0.1 s to come back after being reflected and we will hear the reflection of sound or echo.

Bats have eyes and pretty good eye sight, yet they use echo during flight. While flying a bat uses its throat to produce sound, if there is an obstacle in the front, the sound returns after reflection, and the bat can estimate the distance from the without being obstructed. We cannot hear the sound produced by the bat; because the sound is ultrasound i.e. frequency of the sound is beyond our hearing range. Bats can produce sound of frequency 100 kHz or more.

What is an echo?

The repetition of sound produced by the reflection of sound waves from a wall, mountain, or other obstructing surface and arrives at the listener with a delay after the direct sound is called an echo.

What should be the minimum distance for hearing an echo between the source and the reflector?

For hearing an echo the minimum distance between the source and reflector must be 16.6 meter.

Explain the criterion for hearing an echo.

For hearing an echo of any sound the distance between the source of sound and reflector must be such that the reflected wave can not come back to the listener before a time of 0.1 second. 0.1 second is the persistence period of hearing. If any new sound reaches our ear in this period of hearing. If any new sound reaches our ear in this period we cannot hear it. This is the criterion for hearing an echo.

Variation of Velocity of Sound

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In air, velocity of sound is proportional to the square root of temperature. 

i.e. v ∝√T

Here, the temperature is not Celsius temperature. Temperature in the Kelvin scale.

The velocity of sound does not depend on the air pressure. But it is inversely proportional to the square root of the density of air, So if there is water vapor in the air, its density decreases, hence velocity increases.

Sound is a mechanical wave. It depends on the elasticity of the medium. The nature of liquid and solid is different from air and naturally the velocity of sound is different there. In liquid the velocity of sound is more than that in air and in solid velocity of sound is even more than in liquid.

Velocity of sound in different medium