Sound Wave Properties

Sound

•Sound is a longitudinallongitudinal (Mechanical)wave caused by a vibrating object

•Molecules collide, producing sound

•Examples: Vocal chords, guitar or piano strings, tuning fork, etc.

Longitudinal Wave• Referred to as a PRESSURE WAVE• A sound wave has high pressure and low pressure

regions moving through a medium• The high pressure regions are called compressions,

molecules are compressed• The low pressure regions are called rarefactions,

molecules are spread out

Frequency

• 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 pitch

• The lower the frequency, the lower the pitch

Wavelength

• Wavelength is the distance between two high pressures or two low pressures

• Wavelength and frequency are inversely related

• A short wavelength (high frequency) results in a high pitch

• http://phet.colorado.edu/en/simulation/sound

What we have learned:

1. Sound is a longitudinal wave.

2. Sound requires a medium.

3. Sound travels fastest in solids, slowest in gases.

4. Wavelength and frequency are inversely related.

5. As the frequency of a wave increases, the pitch increases. As the frequency of a wave decreases, the pitch decreases.

Frequency and the human ear• Humans can hear a range of frequencies from 20 Hz to

20,000 Hz• The older you get, the hearing range shrinks• Sound waves with frequencies below 20 Hz are called

infrasonic• Sound waves with frequencies above 20,000 Hz are

called ultrasonic

Hearing Range Frequencies• http://www.movingsoundtech.com/• http://www.noiseaddicts.com/2009/03/can-you-hear-this-

hearing-test/

Amplitude• The human ear is sensitive to difference in pressure

waves• The AMPLITUDE of a sound wave determines it’s

loudness or softness• This means the more energy in a sound wave, the louder

the sound• Sound intensity is a measure of how much energy passes

a given point in a time period• Intensity is measured in decibels

DECIBEL• Every increase of 10 dB has a 10x greater amplitude

• Most people perceive an increase of 10 dB to be about twice as loud as the original sound

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 1020

Jet engine at 30 m 140 dB 1014

Perforation of eardrum 160 dB 1016

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.

Sound Behaviors: Reflection• Reflection of sound results in an echo• http://www.youtube.com/watch?v=sAYt-lf4AWk• Sound waves leave a source, travel a distance, and

bounce back to the origin• Animals, like bats, uses echoes to locate prey• Other uses include determining distance between objects,

echocardiograms• The distance the sound travels to get back to the origin is

2x the distance between the sound source and boundary

Sound Behavior: Refraction• Refraction occurs when sound moves from one medium

to another• The wave bends, and the speed changes

• Even when sound moves from warmer areas to cooler areas, refraction occurs

Sound Behavior: Diffraction• Diffraction occurs when sound waves pass through an

opening or through a barrier• Low pitched sound waves travel farther than high pitched

sound waves• Animals use diffraction for communication• http://video.nationalgeographic.com/video/animals/

mammals-animals/elephants/elephant_african_vocalization/

Velocity• Velocity of sound depends on the medium it travels

through and the phase of the medium• Sound travels faster in liquids than in air (4 times faster in

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

faster in iron than in air)• Sound does not travel through a vacuum (there is no air

so sound has no medium)

Velocity and Temperature• In air at room temperature, sound travels at 343 m/s (at

20°C). This is about 766 mph.• As temperature increases, the velocity of sound increases

v= velocity of sound in air

T=temperature of air in °C

v=331 + (0.6)T

Wave Equation

Example Problems:

1. Sound waves travel at approximately 340 m/s. What is the wavelength of a sound wave with a frequency of 20 Hz?

2. What is the speed of sound traveling in air at 20º C?

3. If the above sound wave has a frequency of 261.6 Hz, what is the wavelength of the wave?

What is the Doppler Effect?• http://molebash.com/doppler/home.htm

Doppler Effect• Sound waves move out in all directions

Definition

•The Doppler effect is a change in the apparent (or observed) frequency due to the motion of the source or the receiver

•Example: As an ambulance with sirens approaches, the pitch seems high. As the ambulance moves by the pitch lowers.

Doppler Effect

• As the wave travels outward, the front of the wave bunches up, producing a shorter wavelength

• We hear a higher

frequency

•The back of the wave spreads out, producing a longer wavelength

•We hear a lower frequency•http://www.sounddogs.com/searchresults.asp?Keyword=Doppler

•Observer AA hears a low pitch (lower frequency)•Observer BB hears the correct pitch (no change in frequency)•Observer CC hears a high pitch (high frequency)

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.youtube.com/watch?v=gWGLAAYdbbc

Uses of the Doppler Effect• Police use Doppler to measure your speed with radar

• A frequency is sent out with a radar gun• The sound wave hits your car and bounces back to the police car• Speed can be determined based on the frequency changes

received

• Radar can be used to determine the speed of baseballs• Astronomers can determine the distance to other galaxies• Bats use Doppler to locate prey

• If the bat is catching the prey, the frequency is high• If the prey is moving away from the bat, the frequency is low

Doppler Equation

fo= frequency heard by the observerfs = frequency from the sourcev= velocity of the sound wavevo = velocity of the observervs= velocity of the sound source

If the sound source and the observer are moving toward each other:

Doppler Equation

fo= frequency heard by the observerfs = frequency from the sourcev= velocity of the sound wavevo = velocity of the observervs= velocity of the sound source

If the sound source and the observer are moving away from each other:

Example• Sitting on the beach at Coney Island one afternoon,

Sunny finds herself beneath the flight path of the airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz flies toward her at a speed of 100 m/s?

Example

A trumpet player plays a C note of 524 Hz while traveling in a convertible at 24.6 m/s. If the car is coming toward you, what frequency should you hear? Assume the temperature is 20°C.

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.

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

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)

Resonance• Resonance occurs when one object vibrates at the same natural frequency of a second object, forcing that second object to vibrate at the same frequency.

• Resonance Demo

Tacoma Narrows Bridge• http://www.youtube.com/watch?v=BmxHxPYc1qc

Types of Resonance• Resonance is the cause of sound production in musical instruments.

• Energy is transferred thereby increasing the amplitude (volume) of the sound.

• 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 resonatorClosed pipe resonator• open end of tube is anti-node• closed end of tube is node

Harmonics of Closed Pipe Resonance

• The shortest column of air that can have an anti-node at ONE end and a node at the OTHER END is ¼ wavelength long.

• This is called the fundamental frequency or first harmonic. (Lowest possible frequency of any object)

• Resonance occurs every 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• both ends are open• both ends are anti-node

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.

Problem

1. 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

L = λ/4

4 x L = λ

4 x .172 = .688 m

v = f λ

340 = f (.688)

f = 494 Hz

Problems

2. 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

Musical Beats and Intervals• Music consists of multiple frequencies being played at the

same time• Resonance occurs and sound is heard at the antinodes• Atlanta Symphony• Any two sounds whose frequencies result in a 2:1 ratio

are said to be separated by an octave and result in a pleasing sound

Beats• A beat occurs when two sound waves of very similar

frequencies interfere with one another

Beats• The beat frequency is always equal to the difference in

frequency of the two notes that interfere to produce the beats

• If two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected

Sound and Hearing• Acoustics is the branch of physics pertaining to sound• The ear converts sound energy to mechanical energy to a

nerve impulse that is then transmitted to the brain• Our ears allow us to perceive changes in pitch• Our ears are sensitive to a particular range of frequencies

between 1,000 – 4,000 Hz.

Anatomy of the EarAnatomy of the Ear

The Outer Ear• The outer ear consists of the earlobe and the ear canal• Sound enters the outer ear as a pressure wave• The outer ear provides protection to the middle ear and

protects the eardrum

Sound starts at the PinnaPinna

Then goes through the auditory canalauditory canal

The Middle Ear• The middle ear is an air-filled cavity that consists of an

eardrum and three tiny, interconnected bones - the hammer, anvil, and stirrup.

• The eardrum is a very durable and tightly stretched membrane that vibrates as the incoming pressure waves reach

• The stirrup is connected to the inner ear

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 Stapes (stirrup)(stirrup)

The Inner Ear• The inner ear consists of a cochlea, the semicircular

canals, and the auditory nerve• The cochlea and the semicircular canals are filled with a

water-like fluid• The fluid and nerve cells of the semicircular canals

provide no role in the task of hearing; they speed up the detection of sound

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 vibrations will stimulate particular stimulate particular hairs inside the hairs inside the cochleacochlea

• 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.