Producing a Sound WaveSound is defined as any vibrating

disturbance in an elastic medium capable of producing an auditory sensation

Sound waves are longitudinal waves traveling through a medium

The particles of the medium vibrates and communicates the energy of vibration to the surrounding medium, usually the air, where the wave travels and is detected as sound

A tuning fork can be used as an example of producing a sound wave

Using a Tuning Fork

As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork

A sinusoidal curve can be used to represent the longitudinal waveCrests correspond to compressions and troughs to

rarefactions

Categories of Sound Waves

Audible wavesLay within the normal range of hearing of the

human ear (Normally between 20 Hz to 20,000 Hz)

Infrasonic wavesFrequencies are below the audible rangeEarthquakes are an example

Ultrasonic wavesFrequencies are above the audible rangeDog whistles are an example

Human Hearing

Pitchhighness or lowness of a sounddepends on frequency of sound wave

• Quality ( Timbre)• depends on the mode of vibration

Human Hearing

Intensityvolume of sounddepends on energy (amplitude) of sound wavemeasured in decibels (dB)

The greater the intensity of sound the farther the sound will travel and the louder the sound will appear.

Music vs. Noise `Music

specific pitches and sound qualityregular pattern

Noiseno definite pitchno set pattern

Various Intensities of SoundThreshold of hearing

Faintest sound most humans can hearAbout 1 x 10-12 W/m2

Threshold of painLoudest sound most humans can tolerateAbout 1 W/m2

Intensity of Sound WavesThe average intensity of a wave is the rate at

which the energy flows through a unit area, A, oriented perpendicular to the direction of travel of the wave

The rate of energy transfer is the powerUnits are W/m2

1 EI

A t A

Intensity Level of Sound WavesThe sensation of loudness is logarithmic in the

human hearThe most common approach to sound intensity

measurement is to use the decibel scaleDecibels measure the ratio of a given intensity I to

the threshold of hearing intensity, so that this threshold takes the value 0 decibels (0 dB).

Io is the threshold of hearing , 216

212 1010

cm

watts

m

wattsI o

decibelsinI

IdBI

o

10log10 1 dB = 1/10 bel

.

dBxmWx

mWxdBinlevel 8.44103log10

/101

/103log10 4

212

28

Solution:

Intensity

A sound has an intensity of

Ex:

28 /103 mWx What is the sound level in dB?

Intensity of a Point Source

Since the intensity varies as 1/r2, this is an inverse square relationship

The average power is the same through any spherical surface centered on the source

To compare intensities at two locations, the inverse square relationship can be used 2

1 22

2 1

I rI r

lists of intensity levels of various sounds

Sound travels through different media.

We hear sound which usually travels through air. Sound travels through other media as well, such as water and various solids.

Sound travels different speeds in different media. Sound typically travels faster in a solid that a liquid and faster in a liquid than a gas.

The denser the medium, the faster sound will travel.

The higher the temperature, the faster the particles of the medium will move and the faster the particles will carry the sound.

NOTE:

Speed of Sound, General

The speed of sound is higher in solids than in gasesThe molecules in a solid interact more strongly

The speed is slower in liquids than in solidsLiquids are more compressible

propertyinertial

propertyelasticv

Speed of Sound in a LiquidIn a liquid, the speed depends on the

liquid’s compressibility and inertia

B is the Bulk Modulus of the liquidρ is the mass density of the liquid

Bv

Speed of Sound in a Solid Rod

The speed depends on the rod’s compressibility and inertial properties

Y is the Young’s Modulus of the materialρ is the mass density of the material

Yv

Speed of Sound in Air

V

=

ρ – mass density

P – Pressure on the gas

= 1 atm = 1.013 x 106dynes /cm2

R – 8.314 J/mol. K

T – absolute temperature

M – molar mass of the gas

= 28.8x10-3kg/mol for air

γ = cp / cv

= 1.4 (diatomic gas)

= 1.67 (monoatomic gas)

Where:

Speed of Sound in Air at a Temperature, t

tsmV

tscmV

o

o

6.0/332

60/200,33

Resonance

Forced Vibrationwhen one vibrating object

forces another object to vibrate at the same frequency

results in a louder sound because a greater surface area is vibrating

used in guitars, pianos, etc.

• object is induced to vibrate at its natural frequency

BeatsBeats are alternations in loudness, due to interferenceWaves have slightly different frequencies and the time

between constructive and destructive interference alternates

The beat frequency equals the difference in frequency between the two sources:

2 1ƒ ƒ ƒb

Beat Frequency

variations in sound intensity produced by 2 slightly different frequencies

both constructive and destructive interference occur

Standing Waves in Air Columns

If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted

If the end is open, the elements of the air have complete freedom of movement and an antinode exists

Resonance in an Air Column Closed at One End

The closed end must be a nodeThe open end is an antinode

There are no even multiples of the fundamental harmonic

1ƒ 1, 3, 5,4n

vf n n n

L

(Closed Tube)

Resonance in Air Column Open at Both Ends

In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency

1ƒ ƒ 1, 2, 3,2n

vn n n

L

(Open Tube)

Doppler EffectA Doppler effect is experienced whenever there is relative

motion between a source of waves and an observer.

Ex:When the source and the observer are moving toward

each other, the observer hears a higher frequencyWhen the source and the observer are moving away from

each other, the observer hears a lower frequency

Assumptions:• The air is stationary•All speed measurements are made relative to the stationary medium

Doppler Effect

As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases

As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower

Doppler Effect, General Equation

Both the source and the observer could be moving

Stationary source of sound, vs=0

Stationary observer, vo = 0

Moving source of sound, vs = - if → (toward the observer)

= + if ← (away from the observer)

Example1. An ambulance travels down a highway at a

speed of 33.5 m/s, its siren emitting sound at a frequency of 400 Hz. What frequency is heard by a passenger in a car travelling at 24.6 m/s in the opposite direction as the ambulance:

a)approach each otherb)pass and move away from each other?

(Take the speed of sound in air to be 345 m/s)

2. A man standing in front of a concrete wall fired a gun and received an echo 5 seconds later upon firing. If the air temperature is 30 oC, how far is the man from the wall?

3. A metal rod 100 cm long is clamped ¼ from one end and rubbed with a piece of rosined cloth to produce sound. The length of powder segment heaps inside the tube is 8 cm. If the air temperature is 20oC, find a) frequency of sound emitted by the rod & b) velocity of sound in the rod

4. A closed pipe at its third harmonic and an open pipe at its second harmonic are vibrating at the same place and produce 4 beats (vps) with the open pipe emitting the louder sound. If the length of the closed pipe is 80 cm and air temperature is 30oC. Find the length of the open pipe.

5. What is the shortest length of a column of air closed at one end so that a sound of 420 Hz can cause it to vibrate? What would be the next shortest length? Assume the speed of sound to be 335 m/s.

6.A railroad is struck by a hammer and an observer hears two sounds, one from air and one from the rail with the time interval of 4 seconds and air temperature of 25⁰C. If the Yrail= 20 X 1011dynes/cm2 and ρrail= 7.8 g/cm3, how far is the source from the observer?

7. An object is dropped into a deep well which has a layer of water in its bottom. If the well is 60 m deep with an air temperature of 20⁰C, how long after the object is dropped will the splash be heard?

8.A police siren emits a sinusoidal wave with frequency fs = 300 Hz. The air temperature is 20⁰C. a) Find the wavelength of the waves if the siren is at rest in the air. b) If the siren is moving at 30 m/s, find the wavelengths of the waves ahead and behind the source.

9. A train travelling at 20 m/s along a straight track passes an observer who is moving in the same direction as the train at 4 m/s. When the train is approaching the observers hears a note of 400 Hz. If the air temperature is 0 ⁰C, what is the frequency of sound heard by the observer as the train passed?