PHY238YLecture 8

Sound waves The speed of sound Traveling sound waves Intensity and sound level

References: Haliday, Resnick, Walker: Fundamentals of Physics, 6th ed., Wiley 2003, Ch. 18 (18.1 – 18.3, 18.5)

Hallett et al.: Physics for the life sciences, 4th ed., Ch.2 (2.1 – 2.5)Thanks to dr. R. Nave for the permission to use some of the pictures from Hyper

Physics: http://hyperphysics.phy-astr.gsu.edu

PHY238YLecture 8

Sound waves are longitudinal

A single-frequency sound wave traveling through air will cause a sinusoidal pressure variation in the air.

The air motion which accompanies the passage of the sound wave will be back and forth in the direction of the propagation of the sound. tkxss m cos

PHY238YLecture 8

The elastic property of a gas or liquid is called bulk modulus

The speed of sound:

density

bulkBwhere

B

propertyinertial

propertyelasticv

modulus

:

PHY238YLecture 8

Sound pressure: Audible sound consists of pressure waves Sound pressure pm is defined as the amplitude of the pressure wave The power carried by the wave is proportional to the square of the amplitude

PHY238YLecture 8

Traveling sound waves: Displacement and

pressure variations

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Sound intensity is

Power/unit area

or: time rate of energy transfer/unit area Many sound intensity measurements are made relative to a standard

threshold of hearing intensity I0, The most common approach to sound intensity measurement is to

measure the sound level on the decibel scale:

2162120 /10/10 cmWattsmWattsI

010log10)(I

IdBI

The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because ~ 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear

PHY238YLecture 8

The threshold of hearing

The measured threshold of hearing curve shows that the sound intensity required to be heard is quite different for different frequencies.

The standard threshold of hearing at 1000 Hz is nominally taken to be 0 dB (it actually is 4 dB)

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Threshold of pain is 120 – 130 dB

The dynamic range of human hearing extends from zero dB to the threshold of pain.

Example: problem 18-2 p. 404 from Halliday/Resnick/Walker

Intensity level (dB)

Ear drum rupture 160

Pain threshold 120-130

Shotgun blast 100

Car horn (6 m distance)

90

City street 75

Typical room 40

Open country 10

Threshold of hearing

0

PHY238YLecture 8

The audible sound: a pressure wave with frequency between 20 Hz and 20,000 Hz and with an intensity above the standard threshold of hearing:

Frequency: 20 Hz - 20,000 Hz (corresponds with pitch) Wavelength (at 20oC in air): 0.0172m – 17.2 m Intensity: 10-12 - 10 W/m2 (0 to 130 dB) Pressure: 2 x 10-5 - 60 N/m2 (2 x 10-10 - .0006 atm) Sounds may be generally characterized by:

Pitch (frequency) Loudness (is NOT simply the intensity level) Quality (timbre – determined by the harmonic content of the

sound)

PHY238YLecture 8

Variation of intensity with distance: the inverse square law:

PHY238YLecture 8

Inverse square law plot