Chapter 14Sound

Chapter 14 Objectiveso Production of a sound waveo Characteristics of sound waveso Ultrasoundo Speed of soundo Intensity of sound waveso Decibelso Types of sound waveso Doppler Effecto Interference of sound waveso Harmonic serieso Resonanceo Standing waves in air columns

Sound Waveso A sound wave can only be

produced when there is a medium to travel through.o airo water

o Sound acts and behaves like a longitudinal waveo The motion of the particles and

the path of the wave travel are in the same direction

Parts of a Sound Waveo Sounds waves travel through a medium

by pushing on the particles.o When the particles are pushed together, it

forms a region of high density called the compression region.

o Following the compression region is a area of lower density called the rarefaction region.

Sound Wave Characteristicso Sound waves are categorized by their

frequency.o The audible range of sound waves are

between 20 Hz and 20,000 Hz.o Hz stands for Hertz

o The SI unit for frequencyo equivalent to 1 s-1

o Sound waves with a frequency below the audible range are called infrasonic.

o Sound waves with a frequency above the audible range are called ultrasonic.

Ultrasoundo Ultrasonic waves are sound waves with

frequencies between 20 kHz and 100 kHzo These waves have such a small

wavelength that they are easy to reflect off an object and read their characteristics after reflection.o Larger waves have more of an arc to provide

for more scattering of the waves after reflection.

o Ultrasound machines bombard human tissues with very high frequency sound waves and then read the intensity of the wave when it returns.o Similar to how radar systems work.

More Ultrasoundo Every time that a sound wave hits the

boundary of two different density materials, part of the wave wants to reflect.o That is why there is mineral oil spread on the

stomach of the mother.o Mineral oil is closer to the density of skin than just

air is.

o There is a formula for the percent return of a sound wave when it experiences this reflection.

0 - 0 + PR = ( ) x 100

2

Speed of Soundo The speed of sound depends on the medium in

which it is traveling through.o That is due to the different compressibilities of the

substances.o More compressible it is, the slower it travels.

o Sound typically travels faster in liquids and even faster in metals.o That is because the molecules are typically much

closer together to create more vibrationso Chart p446

o The speed of sound in air can change based on the temperature.o Higher the temperature, faster the speed

o This is because the molecules are spread out more.

v = (331m/s)Speed of sound in air 0 oC

1 + T/273

Intensityo The rate at which the energy from

the sound wave propagates through a given area is called intensity.o Remember that the rate of energy

transfer is called power.

PI =

AWatts

Meter2

Humans can tolerate sounds from 1 x 10-12 W/m2 up to 1 W/m2.

Decibelso The intensity level of sound are called

decibels.o Represented:

o o Named for Alexander Graham Bell

o Units:o dB

o This scale is a comparison how intense, or loud, the sound wave is compared to normal hearing levelso I0 = 1.0 x 10-12 W/m2

=10 I

I0

log

Wave Propagationo Sound waves are often thought to come

from a single point and propagate in a circular fashion.o Much like throwing a rock in a lake.

o Each arc of the wave is called the wavefront.o The wavefront moves at the same rate.

Intensity of Spherical Waveso Since the waves will travel as a spherical

shell, the area that it approaches is equal to the area of a sphereo 4r2

o Due to the spherical nature, as the wave travels the intensity dissipates by a factor of r2.

PI =

4r2

I1 r22

I2

=r1

2

Doppler Effecto The Doppler Effect is the change in

frequency that is observed between a sound source and a sound receiver that are moving relative to each other.o As the receiver moves toward the source, the

frequency is higher than if the source was not moving.

o As the receiver moves away from the source, the frequency is lower than if the source was not moving.

More About Dopplero The behavior can be different depending

on if the source, the receiver, or both are moving.o If the receiver is moving, it is traveling through

the wavefronts faster than what they are sent, so the frequency goes up.

o Or moving away causes the wavefronts to be heard at a slower rate, or lower frequency.

o If the source is moving towards the stationary receiver, the source is pushing the wavefronts faster than what they are emitted, or higher frequency.

o If the source is moving away, the wavefronts are being pulled apart to make them heard slower, or at a lower frequency.

o Lastly, if both are moving, the effect is exaggerated.

Formulas for Doppler EffectFrequency with receiver in motion

Frequency with source in motion

Frequency with both in motion

’ = ( )v + vo

vSource frequency

Observed frequency

Speed of Receiver’s Motion

’ = ( )v + vs

vSpeed of Source’s Motion

’ = ( )v + vsSpeed of Source’s Motion

v + voSpeed of Receiver’s Motion

Sound Barrier and the Doppler Effect

o As objects approach the speed of sound, the wavefront is virtually equal with the object.

o Once the object is traveling faster than the speed of sound, the wavefront follows the object.

o Remember that sound is traveling through a medium (air)o And that medium has high and low pressure

areas.

o The high pressure area can actually smash the air molecules together fast enough to create a condensation cloud due to the high presence of water in a smaller area.

F-14 Sound Barrier Clip provided by HyperPhysics at GSU

Shockwaveso As an object approaches the speed of sound, the

wavefront becomes more of a conical shapeo Much like the wake of a speed boat in water.

o That conical wave is called a shockwave.o The size of the peak angle of the cone can indicate

how fast the object is traveling compared to the speed of sound.o The sine of the angle between the wavefront and the

object indicates the Mach number.

o The Mach number is the ratio how fast the object is traveling to the speed of sound.o Found by vs over v

o Where v is the speed of sound.

sin = vvs

Velocity of Source

Interference of Sound Waves

o Remember that interference can be either destructive or constructive.

o Constructive interference will be the largest when the waves are a multiple of one full wavelength apart.

o Halfway between nodes is called an antinode.

o If the difference in wavelengths is half a wavelength off, then the two waves will cancel each other out creating destructive interference.

v = λUse this to determine how much you can shift the wave to produce the interference you need.

Standing Waveso A standing wave is a wave that can be

sent down a medium and returned in such a way that it appears to stand still.o One end is free to oscillate and the other is

attached to a fixed point.o Guitar strings

o The position where the string is fixed, or appears to be motionless, is called a node.

Characteristics of Standing Waveso The ends of the strings are nodes because

they are fixed.o The length of the string and the number of

nodes can help determine other characteristics of the waveo string lengtho wavelength

o The lowest frequency of vibration is called the fundamental frequency.o Found by

1 = 1/2L F/μLength of string

Tension in the string

Mass per unit of length of the string

Harmonicso Every time another antinode is added to the

vibration, the frequency must change to keep the vibration going.

o That new frequency falls into the harmonic series of the string.o The harmonic series is an integer multiple of the

fundamental frequency.

o This can be done by either changing the length of the string or the tension in the string.o Pinching the strings on a guitar fret board changes

the length.o Turning the tuning knobs changes the tension.

n = n/2L F/μn is the integer of the harmonic series you are in

= n1

Resonanceo Every object has a natural frequency at which it

vibrates.o When an object is forced to vibrate at the same

frequency as its natural frequency, the object is said to be at its resonant frequency.o This will occur when a vibration is maintained by an

outside force at the maximum amplitude of vibration.o As long as the energy input to maintain vibration is

equal to the energy lost during vibration, the amplitude will remain the same.

o When the forced vibration exceeds the natural frequency, disaster happens!

Tacoma Narrows Bridge Website

Standing Waves in Air Columnso Sound can travel

through air in a closed container which is then reflected back towards the source.

o Because of this reflection, sound interference can be critical.

o So the length of the tube must be adjusted so that the reflection point occurs at a node.

o An open ended container will produce no reflection of the sound wave.

o The length is still critical because it will determine the harmonic series of the wave.