1. Intensity

2. Force to Pressure The pressure wave creates a force on a slice of air.
Wave amplitude s0
Pressure amplitude p0
The amplitudes are related by frequency and wavenumber. A P
P +DP Dx
magnitudes from harmonic waves

3. Force and Intensity Intensity is the power per unit area.
Pressure is force per area.
Expect I = Pv
Use v = s0w
Factor of ½ for average A P
P +DP Dx

4. Threshold of Hearing
The minimum intensity that can be heard by humans is W/m2.
What is the fractional variation in air pressure?
Translate intensity into pressure.
Substitute values.
p0 = 10-5 Pa
Compared to P = 105 Pa this is one part in 10 billion.

5. Intensity Ratio Sound Intensity Ratio over threshold
Threshold W/m2 100
Whisper W/m2 102
Mosquito 10-8 W/m2 104
Talking 10-6 W/m2 106
Traffic 10-4 W/m2 108
Subway 10-2 W/m2 1010
Rock band 100 W/m2 1012
Jet engine 101 W/m2 1013

6. Logarithmic Scale Sound intensity varies over a huge range.
13 orders of magnitude
The exponents are easier to keep track of than the values.
Logarithm of the ratio
Sound Ratio exponent
Threshold 0
Whisper 2
Mosquito 4
Talking 6
Traffic 8
Subway 10
Rock band 12
Jet engine 13

7. Decibel The decibel is a unit that measures the intensity ratio.
Symbol dB
Exponent times 10
Each 10 dB is 10 times more intensity.
Sound dB
Threshold 0
Whisper 20
Mosquito 40
Talking 60
Traffic 80
Subway 100
Rock band 120
Jet engine 130

8. Turn it Down
Your younger sibling is watching TV, and its annoying you at 75 dB. You yell and she turns it down to 60 dB.
By what factor has the intensity decreased?
The difference in logarithms is the ratio of the values
Find the difference in dB
Solve for the intensity
With values I2 / I1 = 0.032

9. Ear Mechanics The ear is collects and amplifies sound.
Initial receiver is the eardrum.
Sensitive to tiny pressure changes
Middle ear transmits the sound through bone.
Act as levels magnifying force by 40
Inner ear (cochlea) separates pitches.
Breaks up superposed waves
Accurate to better than 1% (0.1% with training)
Frequency heard as pitch
Superposition of pitches is timbre

10. Hearing Response
The human ear is sensitive to sounds from 20 Hz – 20 kHz.
Maximum sensitivity is from about 3 kHz to 5 kHz with 120 dB range.
Sensitivity is much worse at low frequencies.
Loudness control for audio equipment boosts bass and treble.

11. Loudness The phon measures the apparent loudness.
Red curves on the graph
At 120 dB most people feel pain.
Rock concert at 4 m.
Jet aircraft at 150 m.
Eardrums burst at 160 dB.