Physics of Sound – Everything you must know about Sound Waves

What is Sound?

The mechanical wave that propagates vibration in a medium is Sound. The propagation medium can be either liquid, solid, or gaseous. It is the fastest in solids, then liquidates and slowest in gas.

This vibration is often audible because of wave pressure in gaseous, liquid, and solid medium. The vacuum does not allow sound to travel. Psychology defines sound as the perception by the brain of the sound pressure reception.

Propagation is a term to describe traveling sound. Three is often a disturbance in the sound pattern which causes energy to travel away from the source and this pattern is the sound wave.

The sound waves are longitudinal and thus the propagation of particles is parallel to the direction of propagated energy waves. Another type of wave is Transverse waves, they travel perpendicular to the direction of propagated waves.

The vibration causes atoms to move back and forth creating high pressure and low pressure in the medium. These pressure zones are compressions and rarefactions respectively.

The transportation of these regions to the surrounding medium leads travel of sound waves from one medium to another. The nature of sound is different because of the source of origin. A guitar will have a different sound than a drum.

Nature Of Sound

The nature of sound mainly depends on five factors – Frequency, Wavelength, Amplitude, Time, and Velocity.

Frequency of Sound

The frequency of the sound wave is the total number of rarefactions and compressions that take place per unit time. The sound of a single frequency creates tone while a mixture of them creates a note. The formula of the frequency of a sound wave is –
f = 1T (f – frequency of a sound wave and T – time period)

Wavelength of Sound

The wavelength is the distance between compression and a followed rarefaction. The formula for the wavelength of the sound is –
λ=vF (f – frequency of the sound wave and v – velocity of the sound wave)

Amplitude of Sound

The maximum disturbance in the sound wave is the magnitude of the sound. And the magnitude of the sound is the amplitude of the sound which is also responsible for measuring energy. Higher amplitude means the energy is higher in the sound wave.

Human and Sound

• Humans have a limited hearing range of sound frequencies. 20 Hz and 20,000 Hz is the frequency range of the human ear. Under ideal laboratory conditions, it can go as low as 12 Hz and high as 20,000 Hz.
• The ear is the organ through which sound reaches the body. The outer shape of the ear resembles a funnel through which the sound enters. There is a canal for sound to pass that ends at a thin membrane called the eardrum.
• The eardrum vibrates as the sound vibration reaches it. It is a rubber sheet-like structure. The eardrum sends the message of sound to our brand through the inner ear making us hear the sound.
• Humans produce sound from the larynx. There are two vocal cords inside through which air passes and produces sound. Men have the longest vocal cord of 20mm approx and for women, it is 15mm.

Time Period

The time period is the total time of completing one vibration. The T denotes time takes in different formulas. The seconds measure the time takes and the Denton is ‘s’. It is usually a reciprocal of wave frequency.

T = v/1

Velocity

The total distance covered by a wave in one second becomes its velocity. Meter, per second measures this quantity.

Velocity = Wavelength × Frequency or v = λv

Speed of Sound

The sound waves propagate a medium at a certain speed and that is the speed of a sound. It is different for different mediums and remains highest in solid as the atoms are in a compact setting.

The distance decides the interaction of atoms in a particle. The energy transfer is faster when there is higher interaction. This is the reason behind the faster sound in solid mediums.

The speed of sound follows this formula –

C = dt (d – distance and t – time taken)

Intensity of Sound

The sound intensity in simple words refers to the passing of energy in one second through per unit area. Watt per meter square measures the sound intensity. It has no relation to human ear sensitivity. And it is an objective quantity.

This is not the same as loudness as loudness looks at the response to the sound by ears. And a pitch is the sound flatness.

The difference between music or noise is also due to intensity. The pleasant sound is music while the unpleasant sound is noise. The formula for Intensity of sound is –

I = PA (I – intensity, P – power and A – area)

Reflection Of Sound

Laws of reflection are applicable to sound as well because it is similar to light reflection. The laws of reflection are –

1. The incident and the normal sound are present in the same place.
2. The angle of incidence = Angle of reflection

When the sound comes in contact with a hard surface, it reflects back to the source. This reflection of sound is the echo. The hard surfactant reflects the sound while the soft one absorbs it.

But in case of low sound frequency, the sound can not reflect back. And when there are multiple echoes from one source, it is reverberation.

Echoes

The sound repetition due to reflection produces an echo. This is common when we find ourselves alone in an empty room and hear our own voice due to sound reflection. Hard surfaces like cliff, mountains, and wall reflect the sound and thus we hear an echo.

The sound surfaces are capable of absorbing the sound. The echo time interval must be 1/10th of a second so that it is audible as two different sounds to human ears.

These intervals allow us to identify the difference between the original and the reflected sound. And the distance between a human and the reflecting surface has to be a minimum of 17.2 meters for an audible echo.

And the air temperature is 20 degrees as the air temperature changes the distance. This is the reason why echos are more on a hot or humid day.

In case the reflecting medium is water, the distance must be 75 meters.

Uses of Echo

• Measuring the sea depth
• Locating the underwater objects
• Investigating the insides of a human body

Reverberation

The multiple reflections of sound from the reflecting surface give rise to Reverberation. There is a building of each reflection which eventually falls as the objects absorb it in closed spaces.

Some may infuse it with echo because of similarities but in the case of reverberation, the distance between sound sources is less an obstacle in reflection is also comparatively low.

Reverberation time is the parameter to measure reverberation quantitatively. It usually looks at the length of time taken in sound decaying by 60 decibels from the starting level.

The time delay in this is not less than 0.1 seconds and the reflection time from surface to the observer is not more than 0.1 seconds. Though the original sound stays in the memory even after all the repetition.

Advantages and Disadvantages of Reverberation

They are responsible for soundproofing musical halls so that there is good music quality in the hall. The sound engineers are responsible for the construction of these specialized halls.

The disadvantage is when the room has no sound-absorbing surface which leads to dying of sound. The listener will have trouble listening to the sound and there will be a loss of articulation.

Application of Reverberation

• Recording Studios
• Chamber reverberator
• Loudspeakers
• Microphones
• Plate reverberator

Reverberations Reduction

The best idea to reduce it is to use sound-absorbing material covering on hard objects. This will allow the reflected sound to decay faster and the listener will be able to hear the original sound. The mineral wool or fiber glasses are porous material that converts sound energy to heat energy by friction.

Vibration of Air Columns

The wind instrument produces sound by vibration inside the air pipes. There is motion inside these tubes making air particles move parallel to the pipe wall. This results in longitudinal wave creation inside the pipe.

This does not depend on closed or open nodes. The nodes are the end of strings to prevent vibrating. This means air doesn’t leave the pipe.

The air particles thus don’t show any motion thus creating a displacement node. There is high pressure inside the tube because of this, thus often referred to as pressure antinodes. In the case of an open pipe end, the air easily leaves and enters.

But the pressure at the end must be equal to room pressure and result in the back and forth movement of particles with high magnitude. This leads to a displacement antinode.

Supersonic and Shock Waves

A sonic boom is a situation when the source speed is faster than the sound speed. It is a type of shock wave where the source generates multiple waves and they get together over time creating a strong sum wave. This phenomenon is very unusual or rare.

An example is a motorboat, the speed of the boat is faster than the wave speed creating a v-shaped bow. A march cone creation takes place in the air when the aircraft has a higher speed than the sound speed. A higher march cone is a sign of faster aircraft speed and vice versa.

Refraction of Sound Waves

As we read above, sound travels faster in warm air. This is because the sound waves bend when they cross air layers of different temperatures. The bending of these sound waves is refraction. The air is warmer near the ground on a summer day and thus the speed of sound near the ground is faster.

The sound bends away from the ground because of refraction. And the case is opposite on a colder winter day. The refraction of sound depends upon the atmosphere density. The density often decreases when there is a temperature rise. This phenomenon has a lot of similarities to the refraction of light.

Diffraction of Sound Waves

The reason why we are able to hear a sound behind the closed door is because of the diffraction of sound. This phenomenon allows sound waves to bend around obstacles. This means that the small keyhole on the door allows sound waves to pass.

We see the diffraction of waves in our daily lives. This is why the thunder lightning sound at a distance sounds higher than the closer one.

The deeper sound wave tones bend near obstacles making you hear a deep rumbling of thunder.

Resonance

Every object has a natural frequency according to its features or characteristics. Resonance is the situation when the object moves at its natural frequency because of vibration received from another system with the same frequency.

Acoustic, mechanic, electric, and optic types of systems are capable of resonance. There is a rise in vibration amplitude due to resonance. It is also very risky in some cases.

Soldiers crossing a suspension bridge always break to avoid resonance and bridge falling. This is also the reason why radios have a particular frequency to tune in.

Interference of Sound Waves

The principle of superposition allows two or more sound waves to get together or combine. This combining of waves is Interference. The superposition principle states “ when two waves are in the same place at the same time, their amplitudes are combined”.

• The constructive interference – total wave magnitude > individual wave
• The Destructive interference – total wave magnitude < individual wave

Electromagnetic Waves

The formation of electromagnetic waves is due to the change in magnetic and electric fields mutually. 299,792,458 m/s is their speed in vacuum. Microwaves and X-rays have electromagnetic waves.

Doppler Effect

Planetary science uses this effect very regularly. It says that “frequency of the type of wave increases with decreasing distance between the source of the wave and observers”. Christian Johann Doppler was behind this concept.

He stated –

• “Waves emitted by a source travelling towards an observer gets compressed”
• “Waves emitted by a source travelling away from an observer get stretched out”

Doppler Effect Formulas

In simpler words, the change in frequency because of relative motion between the observer and the source. The formula for this effect is –
f’ = (v +- vo / v +- vs) f

(Here, v – sound wave velocity, vo – velocity of the observer, vs, the velocity of the source, f’ – observed frequency, and f- actual frequency.) This is the only equation of this effect but it is capable of changing in case of velocity change.

Source Moving Towards the Observer at Rest
The observer velocity is zero thus vo becomes zero. The equation for the observer at rest is –
f’ = (v / v – vs) f

Source Moving Away from the Observer at Rest
The observer velocity is again zero and the source velocity is negative. The equation for this situation is –
f’ = (v / v – (-vs)) f

Observer Moving Towards a Stationary Source
In this situation, the source velocity is zero. This equation for this situation is –
f’ = (v + vo / v) f

Observer Moving Away from a Stationary Source
In this case, the source velocity is zero, and the observer’s velocity is negative. The equation is –
f’ = (v – vo / v) f

Uses of Doppler Effect

• Sirens
• Radar
• Astronomy
• Medical Imaging
• Blood Flow Measurement
• Satellite Communication
• Vibration Measurement
• Developmental Biology
• Audio
• Velocity Profile Measurement

Doppler Effect Limitations

• It is applicable when the velocity of sound is more than the source and observers’ velocities.
• The motion of the observer and source has to be in the same line.

Doppler Effect In Light

The Doppler Effect on light is an apparent change in light frequency because of light’s relative motion between the source and the observer. The sound wave goes under fluctuations spending on the source, medium, and observer.

But light needs no medium and even in vacuum relative speed impacts the effect.

Red Shift and Blue Shift

When the observer is looking at a light source moving away, he receives a lower frequency compared to the original frequency. This results in a shift towards the red end of the spectrum and is the redshift.

And when the light source is moving towards him, the frequency received is higher. He will see the high end of the light spectrum and is the blueshift.

Conclusion

Sound is one of the most important physics topics for multiple competitive exams. These exams are UPSC, RRB, SSC, etc. Some important topics were the nature of sound, the doppler effect, waves, and more.

The General Science paper will definitely have some questions about this topic. And this is important for Prelims as well. This is because it comes under the 9th physics and is present in NCERT books as well.

Candidates will definitely receive reliable and easy-to-understand information from the article above. Aspirants will be better prepared after reading this.

Stay with DataFlair for more such interesting articles.