Physics of Physics of SoundSound

CHHS Physics

Mr. Puckett

SoundSound Sound is the longitudinal wave of

energy through the air that has 3 aspects

– First, It has a source that is vibrating and compressing air molecules

– Second, the air compressions radiate out in waves that carry the energy of the vibration.

Third, the sound is detected by an ear or an instrument.

Sound Waves Sound Waves

Sound waves are produced by the compression and rarefaction of matter.

Sound cannot travel through a vacuum without matter to propagate the wave

LONGITUDINAL WAVESLONGITUDINAL WAVES

Shock WaveShock Wave

It is this sudden buildup of gas pressure that constitutes the nature of an explosion.

The speed at which explosives decompose permits their classification as high or low explosives.

Video: Rocket fuel production plant shock wave. http://www.youtube.com/watch?v=_KuGizBjDXo

Sources of SoundSources of Sound

Stringed Instruments Stringed Instruments When playing a stringed instrument the

length of the string partially determines the frequency of the sound that you hear. Whether its a piano or a guitar or mandolin the principle is the same.

To compute the frequency of a string you use the formula : Ll fl = Lh fh where l is

the low note and h is the high note

Stringed InstrumentsStringed Instruments

Speed of SoundSpeed of SoundThe speed of sound, differs with each

material and temperature it goes through. Standard is 343 m/s at 20oC and 1 atm of pressure.

Only military aircraft and the Concord Jetliner use supersonic ranges of speed. They travel in Mach number speeds which are multiples of the normal speed of sound ( 343 m/s = 1 Mach at standard conditions).

Breaking the Speed of SoundBreaking the Speed of Sound

Breaking the sound barrier was a difficult task until 1947 when Chuck Yeager broke it in a Bell X-1 experimental aircraft.

Breaking the sound barrier produces a shock wave often called a Sonic Boom when the craft outruns its own sound waves and creates a high pressure buildup in front of the aircraft and a trough (low pressure) area toward the rear of the aircraft.

Breaking the Sound BarrierBreaking the Sound Barrier

F-18 Hornet Breaking the Speed F-18 Hornet Breaking the Speed of Soundof Sound

Picture of the shockwave from a jet breaking the speed of sound. You see the Sonic Boom.

The cloud is produced by the compression / condensation of the water vapor out of the air.

Volume of SoundVolume of Sound Loudness or volume is a reflection of the

energy of the compression wave.

1. It is measured in units of Decibels ( named after Alexander Graham Bell) and are described by the equation:

  (dB) = 10 log I / Io

120 dB = 1 Watt /m2 Intensity of spherical wave: I = Power/area = P/4πr2

Volumes of SoundVolumes of Sound Typical sound levels are:

– Whisper 20 dB, – Normal conservation 65 dB, – Siren at 30 m 100 dB, – Rock concert indoor/pain 120 dB, – Jet at 30 m 140 dB. – Sounds greater than 250 dB can kill you. – http://science.howstuffworks.com/question124.htm

How Loud is It?How Loud is It?

Sound is measured in decibels, which is a logarithmic scale. The faintest sound a human can hear is 10 dB, about a pressure difference of 2x10-5 Pa, a sound with 10 times the pressure difference is 20 dB.

Loss of HearingLoss of HearingPermanent hearing loss occurs when sounds

are above 75 dB for long times or 100 dB for short times.

The Navy requires hearing protection above 100 dB and double protection (plugs and ear muffs) above 140 dB

Since this is a logarithmic scale then a 10-2 W/m2 sound is twice as loud as a 10-3 W/m2 sound

Human Ear AnatomyHuman Ear Anatomy

Pitch of SoundPitch of Sound

1. Pitch is the frequency of a sound. High pitches are from high vibrational sources like violin and low pitches are from the bass instruments.

a. The audible range for the normal human ear is 20 Hz to 20,000 Hz. Those with old age, ear infections and loud stereos may have greatly reduced hearing ability.

Pitch of Sound Pitch of Sound continuedcontinued

b. The ultrasonic range is the frequency range above 20,000 Hz that humans generally cannot hear. Dogs and other animals can hear in this range (50,000 Hz) from many miles away. Bats can hear up to 100,000 Hz.

c. The infrasonic range is the range below 20 Hz. The sources for these include earthquakes, thunder, volcanoes and vibrating heavy machinery that damage human organs.

ResonanceResonanceResonance is the natural

frequency at which standing waves occur. In a standing wave the nodes and antinodes are stationary due to constructive interference patterns of waves going to and returning from a node (usually at a fixed point like a bridge or tuning peg like a guitar. ) Article link.

Natural ResonanceNatural ResonanceThe frequency of

energy input that will naturally cause an object to start resonating or vibrating. Example: tuning forks or wind / bridges

Sound HarmonicsSound Harmonics

The Fundamental frequency or First Harmonic and it’s length is one half of the wavelength for an open tube.

L = ½ 1

Overtone is another name for the harmonic wavelengths above the fundamental wavelength and keys in on the number of nodes in the standing wave.

If the vibrating source increases it’s frequency by twice; then the standing wave will show two antinodes. This would be the second harmonic and the length of the standing wave would be equal to the wavelength (L = 2 ).

Third HarmonicsThird Harmonics

The standing wave with three antinodes is called the third harmonic.

The general formula is : L = nn / 2 where n = 1, 2, 3, 4 etc and represent the integer multiples of the fundamental frequency and length. … and the wavelength is = 2L / n

Wave Harmonics GraphWave Harmonics Graph

Frequencies of HarmonicsFrequencies of HarmonicsFor open tube resonators and stringed

instruments, the harmonics are multiples of the frequencies. For example: A guitar string of 500 Hz frequency as its first harmonic / fundamental frequency has a second harmonic of 2 X 500 Hz = 1000 Hz and the third harmonic of 3 X 500Hz = 1500 Hz .

Resonating TubesResonating Tubes

Tubes with at least one opening can resonate when a sound of the correct wavelength causes the air column to vibrate and amplify the sound.

Open and closed tubes used for making sound exhibit different capabilities of making harmonics

Open Tube ResonatorOpen Tube Resonator

An open tube has antinodes at each end of the tube with one or more nodes inside the tube. This is also the model to use with strings.

With the first fundamental tone (first harmonic) the length (L) is = ½ . The second harmonic ( 2 nodes ) has the full wavelength and twice the

frequency. The frequency of each overtone harmonic is an integral multiple of the fundamental frequency.

Resonating TubesResonating Tubes

Closed Tube ResonatorClosed Tube Resonator For a Closed tube, there is always a displacement node at the closed end

because the air there cannot move. Since the distance between a node and the nearest antinode is ¼ then the closed tube has only odd harmonics. It can sound out frequencies 3, 5, 7, times the fundamental frequency, but the even ones are canceled by the node at the closed end.

The equation for a closed tube is L = 1/41 .

Example of a closed tube resonator.

You are hearing the ambient sounds around your environment being amplified by a closed tube resonator.

Quality of SoundQuality of Sound

The Quality of Sound is often called timbre or tonal color. It is the unique sound that makes a flute sound different than a clarinet or French horn or oboe.

The sound we hear is actually a composite of many different wave frequencies using the superposition theory of waves.

Sounds that sound pleasing to the ear are termed “Consonance” and sounds that bring displeasing feelings are called “dissonance”.

Quality of SoundsQuality of Sounds

http://www.phys.unsw.edu.au/jw/sound.spectrum.html

The Beat of SoundsThe Beat of Sounds

If there is a difference in the frequency of two different waves of only a small Hz, then an occasional synchronization of the constructive interference waves will produce a “Beat” .

Beat = Freq1 - Freq2 We don’t always hear the in-between

waves due to destructive interference.

Beat of SoundBeat of Sound

If there is a difference in the frequency of two different waves of only a small Hz, then an occasional synchronization of the constructive interference waves will produce a “Beat” .

Beat = Freq1 - Freq2 We don’t always hear the in-between waves due to destructive

interference.

The Doppler EffectThe Doppler Effect

The Doppler effect refers to the change in pitch of a sound due to the motion of either the source or the listener. If they are approaching each other, the pitch is higher. If they are moving apart, the pitch is lower. This is also the basis of a modern radar system that shows weather movement well. The formula would be:

  f ‘ = f((v +/-vo) / (v -+ vs))

Doppler Effect ApplicationsDoppler Effect Applications

The Doppler EffectThe Doppler Effect

Applications of SoundApplications of Sound

Many new applications in our daily lives use sound waves as the mechanism of action. They include sonar on subs and warnings for severe weather.

Ultrasound is used for diagnostic procedures in medicine to look inside the echo patterns of the sound at high frequency. This is a much better alternative than open exploratory surgery. Bats and dogs use it to detect movements.

Problem Types 1Problem Types 1Remember that frequency and cycle time period

are inverses. f = 1/ TThe velocity of all waves is found by multiplying

the frequency x wavelength: v = f λ and you can find frequency or wavelength by isolating for the particular variable.

Standard velocities of sound in air (343 m/s) and all forms of electromagnetic radiation would be traveling at the speed of light: (3x108 m/s )

Problem Types 1 cont.Problem Types 1 cont.What is the wavelength of a 440 Hz tuning fork

sound? v = f λ 343 m/s = 440 Hz λ λ = 343m/s / 440 Hz = 0.78 meters

What is the wavelength of a radio signal of 82.5 MHz? v = f λ 3x108 m/s = 82.5 X106 Hz λ λ = 3x108 m/s / 82.5 X106 Hz = 3.6 meters wavelength.

Remember: kHz = 103 Hz and MHz = 106 Hz.

Problem Types 2Problem Types 2Straight line distance for sound: d = vt Example: If you see lightening then hear the

sound of thunder 4 seconds later then the original lightening strike was d = 343 m/s X 4 sec = 1372 meters away.

Example: If you throw a rock off a cliff and see it hit the water and hear the sound 1 second later, then the cliff’s height is : d = vt 343 m/s X 1 sec = 343 meters high.

Problem Types 3Problem Types 3Echo's: bats send out sound that bounces off an

object and returns to the bat. Because that is a 2 way round trip, you divide the total time by 2 and then use the equation above: d = vt to find out how far the bat is from the object. Example: a bat hears it’s squeak return 1.2 seconds after it leaves: How far is the bat from the cliff? The 1.2 seconds is a round trip, so divide it by 2 to find the one way distance, and then multiply times the velocity.

D = vt 343 m/s X 0.6 seconds = 206 meters.