WAVES & SOUND

The Physics of Earthquakes

Waves are a disturbance that carries energy from one place to another. There are two types of waves

Types of WavesTransverse (direction

of vibration, perpendicular to propagation of the wave)

Longitudinal (direction of vibration is parallel to the propagation of the wave)

Seismic WavesWhen an earthquake occurs, the shockwave

that travels through the Earth is a seismic wave. This type of wave is a mixture of longitudinal and transverse waves

ExamplesExamples of Transverse waves;

waves in water, radio waves, visible light

Examples of Longitudinal waves;

sound waves, compression waves on a slinkyAcoustics Animations

What are electromagnetic waves?

These are waves that disturb or vibrate electric and magnetic fields.

How do you know if something travels in waves?

Reflection Refraction Diffraction Interference Polarisation (light only)

Interference

This is the addition of two or more waves causing a single resultant wave

Constructive InterferenceConstructive Interference happens when two

or more waves combine to give a resultant wave with greater amplitude than the source wave

Constructive InterferenceConstructive Interference occurs when

waves from two coherent sources meet to produce a wave of greater amplitude.

(Constructive interference occurs when the crests of one wave are over the crests of another wave).

Coherent Waves: Two waves are said to be coherent if they have the same frequency and are in phase.

“In phase” means crests stay over crests and troughs stay over troughs.

Destructive interferenceInterference occurs when waves from two

coherent sources meet to produce a wave of lower amplitude.

(Destructive interference occurs when the crests of one wave are over the troughs of the second wave.

This will happen if one wave is half a wavelength out of phase with respect to the other).

Noise cancelling headphones

Characteristics of a waveReflection is the bouncing of waves off of an obstacle in

their path. Refraction is the changing of direction of a wave as it

travels from one medium to another.Note that when a wave travels from one medium to another its frequency does not change

 Diffraction is the spreading of waves around a slit or an

obstacle.This effect is only significantly noticeable if the slit width

is approximately the same size as the wavelength of the waves.

Periodic time The periodic time of a wave (T) is the time

taken for one complete cycle. Unit: second (s)

Relationship between Periodic Time and frequency

 

T = 1/f

Stationary waves Stationary waves are formed when two

periodic travelling waves of the same frequency and amplitude, travelling in opposite directions, meet.

From the diagram we can see that:1. The distance between two consecutives

nodes is /22. The distance between two consecutive

antinodes is /23. The distance between an anti-node and the

next node is /4

(“nodes” = “no” movement)

How do speed guns work?Speed guns use the

physics of movement on the frequency of waves. This phenomenon was discovered by Christian Doppler and is known as the Doppler Effect.

The Doppler EffectThe Doppler Effect is the apparent change in

frequency of waves due to the relative motion between a wave source and observer. A good example of this is a police siren as it passes you by.

The Doppler EffectConsider a source S emitting a wave with

crests 1, 2, 3 as shown.

The distance between successive crests is the same; therefore the number of crests that pass point A in one second will correspond to the frequency of the wave.

These waves will pass over an observer in equal intervals of time.

This means that the wavelength and therefore the frequency will be the same.

In this case the source is moving to the right while emitting the waves.

The result is that:Ahead of the moving source, the crests are

closer together than crests from the stationary source would be. This means that the wavelength is smaller and the frequency is greater.

Behind the moving source, the crests are further apart than crests from the stationery source would be.

This means the wavelengths are greater and therefore the frequency is less.

 

The Doppler EffectThe speed gun emits radio waves which

bounce off the car then analysed by the gun using the formula for the Doppler Effect;

uc

fcf

Formula:

f” = apparent frequencyf = actual frequencyc = speed of the waveu = speed of the moving source

Remember that the sign below the line is minus if the source is moving towards the observer – ‘Minus Is Towards’ (MITS)

Applications of the Doppler EffectOther applications of the Doppler Effect include red shift of stars (using wavelength instead of

frequencies) and radar used by bats and dolphins.Ultrasound (blood movement or heartbeat of foetus)Weather forecasting.Note: The noise from a racing car as it approaches and then moves away from an observer is an example of the Doppler effect. But it is not an application!!

Demonstration of the Doppler effectThe Doppler effect for sound waves is

dramatically demonstrated by swinging a ringing tuning fork around your head.

The Doppler Effect – Exam questionsNote that when explaining the effect, the

marking scheme looks for four separate points here:

A series of non-concentric circles.Direction of motion of source and position of

observer must be indicated.Reference to apparent change in wavelength.Reference to resulting apparent change in

frequency.

SoundWe know from the last section that sound is a wave motion. We know this because sound undergoesReflection (echoes)Diffraction (you can hear around corners)Refraction (Explains why sometimes we don’t

hear thunder from far away lightning ) Interference (see next demonstration)

Refraction in SoundDifferent layers of air are at different

temperatures, and sound travels at different speeds in the different layers (quicker in warmer air which is closer to the ground, as a result the sound wave bends away from the ground).

To demonstrate Interference of soundMethod 1: Using a Signal Generator and Loudspeakers

Walking slowly from X to Y, you will notice the loudness of the sound increasing and decreasing at regular intervals.

This is because sound waves from the two speakers will interfere both constructively and destructively, along the path XY.

NB: You must make reference to a signal generator or sound from each speaker having the same frequency.

Method 2: Using a Tuning ForkPlace a vibrating tuning fork beside your ear

and rotate it. Again, the loudness of the sound will increase

and decrease at regular intervals, this time due to interference between the compressions and rarefractions, as the legs of the tuning fork moves in and out.

Note 1: You don’t have to understand why this works.

Note 2: Either demonstration is acceptable for exam purposes.

To show that Sound needs a medium to travel throughSet up the Bell-Jar – the bell can be heard

ringing. Remove the air from the Bell-Jar using a

vacuum pump.Result: While the bell can still be seen to be

ringing, the sound gets quieter until eventually nothing can be heard

Loudness & PitchThe loudness of the sound wave depends on

the amplitude of the wave

the pitch of a note depends on the frequency.

How does a singer shatter a glass with a high pitched note? Natural frequency is the frequency with

which a body will vibrate at when vibrating freely.

If you have two guitar strings tuned to the same note and pluck one of the strings the other will vibrate. This is known as resonance. The singer sings the note at the same frequency as the natural frequency of the glass and it vibrates enough to shatter.

Factors which determine the Natural Frequency of a Stretched StringFrequency is inversely proportional to the length of

the string: f 1/L,Frequency is directly proportional to the square

root of the tension in the string; f T,Frequency is inversely proportional to the square

root of the mass per unit length of the string; f 1/µ .µ (pronounced “meu”) represents ‘mass per unit length’ and is a bit like saying ‘the density of the string material’)

Putting these together, and letting the proportional constant = ½ (just because it is!) we get

Fundamental FrequencyThe fundamental frequency is denoted by the

formula;

T

lf

2

1

Natural frequencyRattling Windows Passing vehicles producing vibrations matching the natural frequency of a window in a nearby building can cause the windows to resonate.

Vibrations in Washing Machines Washing machines may vibrate violently at particular speeds because resonance occurs when the frequency of the rotating drum equals a natural frequency of the body of the machine. There are usually several natural frequencies at which resonance can occur.

ResonanceThe rapid amplification of oscillation when a

periodic force is applied at the same frequency of the body

Examples of Resonance: Washing Machines at a particular speed, Microwave Ovens

Water Molecules in a microwaveVocal chordsTacoma Bridge

To Demonstrate Resonance

Use two identical tuning forks and a sound-board.Start one fork vibrating, place it on the sound-

board and notice the sound.Place the second tuning fork on the sound-board

and then stop the first tuning fork from vibrating.The second fork can now be heard.ExplanationThe vibrations were passed from the first tuning

fork via the sound-board to the second tuning fork.

How do wind instruments work?

Like with guitar strings standing waves are set up in the tube. A standing wave is a wave that remains in a constant position and is made up of a series of nodes and antinodes

Ruben’s Tube

HarmonicsWhen an object is vibrating at its natural

frequency it is also refered to as the fundamental frequency.

Harmonics are multiples of the fundamental frequency.

By placing your finger over certain holes in the instrument different notes and harmonics can be produced.

OvertonesFrequencies which are multiples of a given

frequency are called overtones.

If f is the first frequency, then 2f is its first overtone; 3f is its second overtone etc.

In a pipe with one end closed only odd numbered harmonics may be present

In an open pipe all harmonics may be present

QualityThe quality of a note describes the shape of

the sound wave and it depends on the number and amplitude of the harmonics present.

The quality of a note depends upon the number of overtones present in the note and the relative strengths of those different overtones.Link wave game guitar

Visualise standing waves on solids

Why can’t your teacher hear that high pitched ring on your mobile phone?

The threshold of hearing is the smallest sound intensity detectable by the average human ear at a frequency of 1kHz. The frequency limits of audibility are between 20Hz and 20kHz. The upper limit decreases with age therefore they may not be heard by your teacher depending on their age!

Sound Intensity LevelThe sound intensity level is a scale that

comprises a particular sound intensity to the threshold of hearing and is measured using the decibel scale. (named after Alexander Graham Bell).

Sound Intensity is defined as power per unit area.

The unit of Sound Intensity is therefore the Watt per metre squared (Wm-2)

Given that the sound-wave expands equally in all directions (like a spherical balloon being blown up) then it follows that the area it is passing through is the surface area of a sphere: Area = 4πr2.

Threshold of Hearing Is the smallest sound intensity detectable by the average human ear at a frequency of 1KHz.Its value is 1 x 10-12 Wm-2.

Sound Intensity LevelHuman hearing falls roughly in the range 10

W m-2 (the Threshold of Hearing) to 1 W m-2 (the loudest, called the Threshold of Feeling)

The size of this range is enormous and is very impractical.

We therefore use a different set of numbers which basically compact the Sound Intensity scale.These numbers are called Sound Intensity levels and are measured in Decibels (dB)

Decibel scale

Examples of Sound Intensity LevelWhisper = 20 dBiPod at max volume = 100 dBThreshold of Pain = 130 dBPerforation of Eardrum = 160 dB

Note: Doubling the Sound Intensity increases the Sound Intensity Level by 3dB.

Decibel Adjusted dB(A) Scale The decibel adjusted scale is used

because it is adapted to the ear’s frequency response.The ear is most sensitive to frequencies between 2000 Hz and 4000 Hz and the Decibel Adjusted scale takes this into account.The sound-level meter used by environmental engineers has a decibel adjusted scale.

Speed of Sound in different media

In general, the speed of sound of sound in a solid is greater than in a liquid, which in turn is greater than that for a gas.

The speed of sound in air (at a temperature of 20 0C) is 343 m s-1.