Sound Waves

• Vibration of a tuning fork

http://www.ndt-ed.org/EducationResources/HighSchool/Sound/hs_sound_index.htm

Pressure Waves

•Sound waves is usually analyzed from the point of view of pressure because the pressure is easier to measure than displacement.

Compression (pressure higher)Rarefaction (pressure lower)

Atmospheric pressure

Pressure and Displacement in Sound Waves

• A sound wave can be described in terms of displacements of particles in the medium or in terms of pressure fluctuations.

Displacement Pressure fluctuation

The displacement graph is π/2 out of phase with the pressure graph.

Position

http://squ1.com/archive/index.php?sound/properties.html

Variation of the air pressure in an air column

Pressure and displacement in an air column

• When the air is constrained to a node, the air motion will be alternately squeezing toward that point and expanding away from it, causing the pressure variation to be at a maximum.

http://www.walter-fendt.de/ph11e/stlwaves.htm

Frequency Spectrum of Sound Waves

1 10 102 103 104 105 106 107 108 /Hz

Frequency in Hz on a log scale

20 kHz20 Hz

Range of sound frequenciesheard by human ears

UltrasoundSubsonic

Used in medicaldiagnosis

Note that the audible range varies somewhat from one individual to another.

The Speed of Sound

• Typically there are two essential types of properties which effect wave speed.– Inertial properties (e.g. mass density, )

• The greater the inertia the slower the wave.

– Elastic properties (e.g. Young modulus, E)• The higher the elasticity the faster the wave.

• Speed of Sound in a long solid rod

E

v Where E is the Young modulus and is the density of the solid rod.

Speed of Sound in air

• The speed of a sound wave in air depends upon the properties of the air– the temperature

• and the temperature will affect the strength of the particle interactions (an elastic property).

– the pressure• The pressure of air (like any gas) will affect the mass

density of the air (an inertial property).

v = 331 + 0.61 TC (m s-1)

Measuring the Speed of Sound in Air (1)

• The speed of sound in air can be measured by– Stationary waves pattern established between a

loudspeaker and a metal reflector.– Using a resonance tube (or Kundt’s tube)

Glass Tube

Signal generator

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/kundtosc.html

Measuring the Speed of Sound in Air (2)

http://www.picotech.com/applications/sound.html

Measuring the speed of sound using echoes

http://www.cdli.ca/courses/phys2204/unit04_org02_ilo02/b_activity.html

http://serc.carleton.edu/quantskills/teaching_methods/uncertainty/examples/example2.html

Speed of Sound in Various Materials

Material Speed of sound /m s-1

Air (0 oC) 331Air (20 oC) 344Helium (20 oC) 999Hydrogen (20 oC) 1330Water (0 oC) 1400Water (20 oC) 1480Mercury (20 oC) 1450Aluminium 6420Steel 5940Lead 1960

Effect of temperature and relative humidity on the speed of sound in air

Loudness

• Loudness is a sensation in the consciousness of a human being.• The assessment of loudness is controlled by(1) The sound wave intensity, which depends on

(a) the square of the amplitude,(b) the frequency, (c) the speed,

(2) The sensitivity of the hearer to the particular frequency being sounded.

2222 fvAI

(d) the density of the medium.

Energy Transport and the Amplitude of a Wave

• The energy transported by a wave is directly proportional to the square of the amplitude of the wave.

E A2

Sound Intensity

• The sound intensity in a specified direction is the rate of sound energy flowing through a unit area normal to that direction. The sound intensity is normally measured in watt per square metre (W/m2).

Energy flow A Area

PowerI

Unit : W m-2

Variation of Intensity with Distance (1)

• The intensity decreases away from the source because

- the energy is distributed through a larger volume, (For a point source and isotropic medium the intensity will obey the inverse square law.) - of attenuation: the wave energy is gradually converted by an imperfectly elastic medium into the internal energy of the medium’s molecules.

Variation of Intensity with Distance (2)

• If the power output is P, then the average intensity, through a sphere with radius r is

24 r

PI

r

• As the wave moves outward, the energy it carries is spread over a larger and larger area since the surface area of a sphere of radius r is 4r2.

Variation of Intensity with Distance (3)

• If a source of sound can be considered as a point,

Intensity level

Distance

2

1

rI

where r is the distance from the source.

Intensity Level (Decibel)

• The intensity level of a sound wave is defined by

oI

Ilog10 where I = the intensity of sound,

Io= 1 pW m-2 (Threshold of hearing)

Unit : decibel (dB)

• The dB-scale is a logarithmic, the reason for measuring sound this way is that our ears (and minds) perceive sound in terms of the logarithm of the sound pressure, rather than the sound pressure itself.

http://www.teachersdomain.org/resource/lsps07.sci.phys.energy.amplitude/

Difference in Sound Intensity Level

• Consider two loudspeakers playing sounds with power P1 and P2 respectively.

• The difference in decibels between the two is defined to be

1

2log10P

P

http://www.phys.unsw.edu.au/jw/dB.html#definitioin

Intensity of Various Sounds

1 × 10-120 Threshold of hearing

1 × 10-1110 Rustle of leaves

1 × 10-1020 Whisper

1 × 10-840 Quiet radio

3 × 10-665 Ordinary conversation, at 50 cm

1 × 10-570 Busy street traffic

3 × 10-575 Automobile moving at 90 km h-1

1 × 10-2100 Siren at 30 m

1120 Loud indoor rock concert

1120 Threshold of pain

100140 Jet plane at 30 m

Intensity/W m-2Intensity Level/dBSource of the Sound

Sensitivity of Human Ear as a Function of Frequency

Each curve represents sounds that seemed to be equally loud.

Note that the ear is most sensitive to sounds of frequency between 2 kHz and 4 kHz.

http://www.phys.unsw.edu.au/jw/hearing.html

Sound Proofing (1)

• Soundproofing of a room involves the isolation of that room from audible sound from the outside and may be taken to include the acoustic damping of the room itself.• Preventing the entrance of sound from the outside is accomplished by -sealing openings, -making the walls absorbent of sound, and -minimizing the passage of sound energy through the solid structures of the walls.

Sound Proofing (2)

• Sound absorbing materials such as foam insulation in the walls help with both the sealing and absorbing of mid-range to high frequency sounds.