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Sound Waves. Vibration of a tuning fork. Compression (pressure higher). Rarefaction (pressure lower). Pressure Waves. Sound waves is usually analyzed from the point of view

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Sound Waves

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Sound waves l.jpg
Sound Waves

  • Vibration of a tuning fork

Pressure waves l.jpg

Compression (pressure higher)

Rarefaction (pressure lower)

Pressure Waves

  • Sound waves is usually analyzed from the point of view

  • of pressure because the pressure is easier to measure

  • than displacement.

Atmospheric pressure

Pressure and displacement in sound waves l.jpg

Pressure fluctuation


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.


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

pressure graph.

Pressure and displacement in an air column l.jpg
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.

Frequency spectrum of sound waves l.jpg

Used in medical


20 Hz

20 kHz

Range of sound frequencies

heard by human ears



Frequency Spectrum of Sound Waves

Frequency in Hz on a log scale

1 10 102 103 104 105 106 107 108 /Hz

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

The speed of sound l.jpg
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

Where E is the Young modulus and

 is the density of the solid rod.

Speed of sound in air l.jpg
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 l.jpg

Glass Tube



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)

Measuring the speed of sound in air 2 l.jpg
Measuring the Speed of Sound in Air (2)

Measuring the speed of sound using echoes l.jpg
Measuring the speed of sound using echoes

Loudness l.jpg
Loudness sound in air

  • 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,

(d) the density of the medium.

(2) The sensitivity of the hearer to the particular frequency

being sounded.

Energy transport and the amplitude of a wave l.jpg
Energy Transport and the Amplitude of a Wave sound in air

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

E  A2

Sound intensity l.jpg
Sound Intensity sound in air

  • 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

Unit : W m-2

Variation of intensity with distance 1 l.jpg
Variation of Intensity with Distance (1) sound in air

  • 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 l.jpg
Variation of Intensity with Distance (2) sound in air

  • 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 4r2.


  • If the power output is P,

  • then the average intensity,

  • through a sphere with

  • radius r is

Variation of intensity with distance 3 l.jpg

Intensity level sound in air


Variation of Intensity with Distance (3)

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

where r is the distance from the source.

Intensity level decibel l.jpg
Intensity Level (Decibel) sound in air

  • The intensity level of a sound wave is defined by

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.

Difference in sound intensity level l.jpg
Difference in Sound Intensity Level sound in air

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

  • Thedifference in decibelsbetween the two is defined to be

Intensity of various sounds l.jpg
Intensity of Various Sounds sound in air

Source of the Sound

Intensity Level/dB

Intensity/W m-2

Jet plane at 30 m



Threshold of pain



Loud indoor rock concert



Siren at 30 m


1 × 10-2

Automobile moving at 90 km h-1


3 × 10-5

Busy street traffic


1 × 10-5

Ordinary conversation, at 50 cm


3 × 10-6

Quiet radio


1 × 10-8



1 × 10-10

Rustle of leaves


1 × 10-11

Threshold of hearing


1 × 10-12

Sensitivity of human ear as a function of frequency l.jpg
Sensitivity of Human Ear as a Function of Frequency sound in air

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.

Sound proofing 1 l.jpg
Sound Proofing (1) sound in air

  • 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 l.jpg
Sound Proofing (2) sound in air

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

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