SoundSound

Chapter 15Chapter 15

Topics for SoundTopics for Sound• Sound wave propertiesSound wave properties

• Speed of soundSpeed of sound

• EchoesEchoes

• BeatsBeats

• Doppler shiftDoppler shift

• ResonanceResonance

• Anatomy of EarAnatomy of Ear

Sound Wave Sound Wave PropertiesProperties

Sound Waves are Sound Waves are Longitudinal WavesLongitudinal Waves

The air molecules shown below are either The air molecules shown below are either compressed together, or spread apart. This compressed together, or spread apart. This creates alternating high and low pressure.creates alternating high and low pressure.

FrequencyFrequency• The frequency of a sound wave (or any

wave) is the number of complete vibrations per second.

• The frequency of sound determines its pitch.

The higher the frequency, The higher the frequency, the higher the pitchthe higher the pitch

WavelengthWavelength• Wavelength is the distance between two high pressures, or

two low pressures. This property is dependent on the velocity of the sound and it’s frequency.

• Wavelength and frequency are inversely related.• Short wavelength (high frequency) results in a high pitch.

Frequency and the human ear

• A young person can hear pitches with frequencies from about 20 Hz to 20000 Hz. (most sensitive to frequencies between 1000 and 5000 Hz).

• As we grow older, our hearing range shrinks, especially at the high frequency end.

• By age 60, most people can hear nothing above 8000 Hz.• Sound waves with frequencies below 20 Hz are called

infrasonic.• Sound waves with frequencies above 20000 Hz are called

ultrasonic.

The Amplitude of a Sound The Amplitude of a Sound Wave Determines its Wave Determines its loudness or softnessloudness or softness

Velocity of SoundVelocity of Sound

The velocity of sound depends onThe velocity of sound depends on

• the medium it travels through the medium it travels through

• the temperature of the mediumthe temperature of the medium

• Sound travels faster in liquids than Sound travels faster in liquids than in air (4 times faster in water than in in air (4 times faster in water than in air)air)

• Sound travels faster in solids than in Sound travels faster in solids than in liquids (11 times faster in iron than liquids (11 times faster in iron than in air)in air)

• Sound does not travel through a Sound does not travel through a vacuumvacuum ( (there is no air in a vacuum there is no air in a vacuum so sound has no medium to travel so sound has no medium to travel through)through)

• The speed depends on the elasticity The speed depends on the elasticity and density of the medium.and density of the medium.

• In air at room temperature, sound In air at room temperature, sound travels at 343m/s (~766 mph)travels at 343m/s (~766 mph)

• v = 331 m/s + (0.6)Tv = 331 m/s + (0.6)T– v: velocity of sound in airv: velocity of sound in air– T: temperature of air in T: temperature of air in ooCC

• As temperature increases, the velocity of sound increases

Effects of Temperature

Relationship between Relationship between velocity, frequency, and velocity, frequency, and

wavelengthwavelength

• V = V = ff• V = velocity of soundV = velocity of sound = wavelength of sound= wavelength of sound

• f = frequency of soundf = frequency of sound

Echoes: Echoes: REFLECTIONREFLECTION

Echoes are the result of Echoes are the result of the reflection of soundthe reflection of sound

Sound waves leave a source, Sound waves leave a source, travel a distance, and bounce travel a distance, and bounce back to the origin.back to the origin.

Things that use echoes...

• Bats

• Dolphins/ Whales

• Submarines

• Ultra sound

• Sonar

REFRACTION OF WAVES

Refraction of Sound

• as the sound wave

transmits into the

warmer air at lower

levels, they change

direction, much like

light passing through a prism

DIFFRACTION:THE BENDING OF WAVES

THROUGH A SMALL OPENING

BENDING OF A WAVE

Sound waves move out like this:

•http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

But when they move, the front of the wave gets bunched up (smaller wavelength) and

the back of the wave starts to expand (larger wavelength):

•http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

Observer CC hears a high pitch (high frequency)

Observer BB hears the correct pitch (no change in frequency)

Observer AA hears a low pitch (lower frequency)

•http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

When the source goes faster, the wave fronts in the front of the source start to bunch up closer and closer together,

until...

The object actually starts to go faster than the speed of sound. A sonic boom

is then created.

•http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

Doppler Effect

• The doppler effect is a change in the apparent frequency due to the motion of the source or the receiver.

• Example: As an ambulance with sirens approaches, the pitch seems higher. As the object moves by the pitch drops.

Police use the Doppler Shift when measuring your speed with radar

• A frequency is sent out of the radar gun

• The sound wave hits the speeding car

• The frequency is changed by the car moving away from the radar and bouncing back

• The amount the frequency changes determines how fast you are going

• The faster you are going, the more the frequency is changed.

Equation that describes the doppler effect.

fd = fs (v + vd) (v - vs)

fs is the actual frequency being emittedfd is the perceived frequency as the source approaches or

recedesvd is (+) if the observer moves toward the sourcevd is (-) if the observer moves away from the sourcevs is (+) if the source moves toward the observervs is (-) if the source moves away from the observer

Example

• Sitting at Six Flags one afternoon, Mark finds himself beneath the path of the airplanes leaving Hartsfield International Airport. What frequency will Mark hear as a jet, whose engines emit sounds at a frequency of 1000 Hz, flies toward him at a speed of 100 m/sec? (temp is 10oC)

Solution

• v = 331 + (0.6)T

v = 331 + (0.6)(10)

v = 337 m/s

• fd = fs(v + vd) f = ?

(v – vs) fs = 1000 Hz

vd = 0 m/s

vs = 100 m/s

Solution

f= 1000 (331 + 0)

(331 – 100)

f = 1430 m/s

SOUND INTENSITY:

THE LOUDNESS OF SOUND

Sound Intensity

• The intensity of a sound is the amount of energy transported past a given area in a unit of time.

• Intensity = power/area• The greater the amplitude, the greater the rate at

which energy is transported-the more intense the sound

• Intensity is inversely related to the square of the distance. As distance increases, the intensity decreases.

Threshold of Hearing

• The human ear is sensitive to variations in pressure waves, that is, the amplitude of sound waves.

• The ear can detect wave amplitudes of 2x10-5 Pa up to 20 Pa.

• The amplitudes of these waves are measured on a logarithmic scale called sound level.

• Sound level is measured in decibels (dB).

DECIBEL

• MEASURES THE LOUDNESS OF SOUND

• RELATES TO THE AMPLITUDE OF THE WAVE

• EVERY INCREASE OF 10dB HAS 10x GREATER AMPLITUDE

Source of Sound Level (dB) Increase over Threshold

Threshold 0 dB 0

Normal Breathing 10 dB 10

Whisper 20 dB 100

Normal Conversation 60 dB 106

Busy street traffic 70 dB 107

Vacuum cleaner 80 dB 108

Average factory 90 dB 109

IPod at maximum level 100 dB 1010

Threshold of pain 120 dB 1012

Jet engine at 30 m 140 dB 1014

Perforation of eardrum 160 dB 1016

A SOUND 10 TIMES AS INTENSE IS PERCEIVED AS BEING ONLY TWICE

AS LOUD

NOISE POLLUTION

· Prolonged exposure to noise greater than 85-90 dB may cause hearing loss

  · Brief exposures to noise sources of 100-130 dB can cause hearing loss

· A single exposure to a level of 140 dB or higher can cause hearing loss

Hours Per Day Noise Level (dB)  8 90 4 95 2* 100* 1 105 0.5 110

EXPOSURE TO LOUD NOISE

Reducing Sound Intensity

• Cotton earplugs reduce sound intensity by approximately 10 dB.

• Special earplugs reduce intensity by 25 to 45 dB.• Sound proof materials weakens the pressure

fluctuations either by absorbing or reflecting the sound waves.

• When the sound waves are absorbed by soft materials, the energy is converted into thermal energy.

ResonanceResonance

Natural Frequency

• Nearly all objects when hit or disturbed will vibrate.

• Each object vibrates at a particular frequency or set of frequencies.

• This frequency is called the natural frequency.• If the amplitude is large enough and if the natural

frequency is within the range of 20-20000 Hz, then the object will produce an audible sound.

Timbre

• Timbre is the quality of the sound that is produced.

• If a single frequency is produced, the tone is pure (example: a flute)

• If a set of frequencies is produced, but related mathematically by whole-number ratios, it produces a richer tone (example: a tuba)

• If multiple frequencies are produced that are not related mathematically, the sound produced is described as noise (example: a pencil)

Factors Affecting Natural Frequency

• Properties of the medium

• Modification in the wavelength that is produced (length of string, column of air in instrument, etc.)

• Temperature of the air

Resonance

• Resonance occurs when one object vibrates at the same natural frequency of a second object, forcing that second object into vibrational motion.

• Example: pushing a swing• Resonance is the cause of sound production in

musical instruments.• Energy is transferred thereby increasing the

amplitude (volume) of the sound.

• http://www.pbs.org/wgbh/nova/bridge/meetsusp.html

Types of Resonance

• Resonance takes place in both closed pipe resonators and open pipe resonators.

• Resonance is achieved when there is a standing wave produced in the tube.

• Closed pipe resonators– open end of tube is anti-node– closed end of tube is node

• Open pipe resonators– both ends are open– both ends are anti-nodes

Closed pipe resonatorClosed pipe resonator

Harmonics of Closed Pipe Resonance

• The shortest column of air that can have a pressure anti-node at the closed end and a pressure node at the open end is ¼ wavelength long. This is called the fundamental frequency or first harmonic.

• As the frequency is increased, additional resonance lengths are found at ½ wavelength intervals.

• The frequency that corresponds to ¾ wavelength is called the 3rd harmonic, 5/4 wavelength is called the 5th harmonic, etc.

Open pipe resonatorOpen pipe resonator

Harmonics of Open Pipe Resonance

• The shortest column of air that can have nodes (or antinodes) at both ends is ½ wavelength long. This is called the fundamental frequency or first harmonic.

• As the frequency is increased, additional resonance lengths are found at ½ wavelength intervals.

• The frequency that corresponds to a full wavelength is the second harmonic, 3/2 wavelength is the third harmonic, etc.

Problems

1. Matt is playing a toy flute, causing resonating waves in a open-end air column. The speed of sound through the air column is 336 m/s. The length of the air column is 30.0 cm. Calculate the frequency of the first, second, and third harmonics.

Solution

1. L = λ/2

2 x L = λ

2 x .30 = .60 m

v = f λ

336 = f (.60)

f = 560 Hz. (first harmonic)

2nd harmonic = 560 + 560 = 1120 Hz.

3rd harmonic = 1120 + 560 = 1680 Hz

Problem

2. Tommy and the Test Tubes have a concert this weekend. The lead instrumentalist uses a test tube (closed end air column) with a 17.2 cm air column. The speed of sound in the test tube is 340 m/s. Find the frequency of the first harmonic played by this instrument.

Solution

2. L = λ/4

4 x L = λ

4 x .172 = .688 m

v = f λ

340 = f (.688)

f = 494 Hz

BeatsBeats

A beat occurs when sound waves of two different (but very much alike) frequencies are

played next to each other. The result is constructive and destructive interference at

regular intervals.

•This oscillation of wave amplitude is called a beat.

•The frequency of a beat is the magnitude of difference between the frequencies of the two waves, f= fA – fB

•See example problem 10 on p. 367.

Anatomy of the EarAnatomy of the Ear

Sound starts at the PinnaPinna

Then goes through the auditory canalauditory canal

The sound waves will then vibrate the Tympanic MembraneTympanic Membrane (eardrum) which

is made of a thin layer of skin.

The tympanic membrane will then vibrate

three tiny bones: the Malleus (hammer)Malleus (hammer), the Incus (anvil)Incus (anvil), and the Stapes (stirrup)Stapes (stirrup)

The stapes will then vibrate the

CochleaCochlea

Inside look of the Cochlea• The stapes vibrates the The stapes vibrates the

cochleacochlea

• The frequency of the The frequency of the vibrations will stimulate vibrations will stimulate particular hairs inside particular hairs inside the cochleathe cochlea

• The intensity at which The intensity at which these little hairs are these little hairs are vibrated will determine vibrated will determine how loud the sound is.how loud the sound is.

• The auditory nerve will The auditory nerve will then send this signal to then send this signal to the brain.the brain.