1. Intensity

2. Force to Pressure  The pressure wave creates a force on a slice of air. Wave amplitude s 0 Pressure amplitude p 0  The amplitudes are related by frequency and wavenumber. P +  P P A xx 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 = s 0  Factor of ½ for average P +  P P A xx

4. Threshold of Hearing  The minimum intensity that can be heard by humans is 10 -12 W/m 2.  What is the fractional variation in air pressure?  Translate intensity into pressure.  Substitute values. p 0 = 10 -5 Pa  Compared to P = 10 5 Pa this is one part in 10 billion.

5. Intensity Ratio  SoundIntensityRatio over threshold  Threshold10 -12 W/m 2 10 0  Whisper10 -10 W/m 2 10 2  Mosquito10 -8 W/m 2 10 4  Talking10 -6 W/m 2 10 6  Traffic10 -4 W/m 2 10 8  Subway10 -2 W/m 2 10 10  Rock band10 0 W/m 2 10 12  Jet engine10 1 W/m 2 10 13

6. Logarithmic Scale  Sound intensity varies over a huge range. 13 orders of magnitude13 orders of magnitude  The exponents are easier to keep track of than the values. Logarithm of the ratioLogarithm of the ratio  SoundRatio exponent  Threshold0  Whisper2  Mosquito4  Talking6  Traffic8  Subway10  Rock band12  Jet engine13

7. Decibel  The decibel is a unit that measures the intensity ratio. Symbol dBSymbol dB Exponent times 10Exponent times 10  Each 10 dB is 10 times more intensity.  SounddB  Threshold0  Whisper20  Mosquito40  Talking60  Traffic80  Subway100  Rock band120  Jet engine130

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 I 2 / I 1 = 0.032 next