Intensity.

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Presentation transcript:

Intensity

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

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

Threshold of Hearing The minimum intensity that can be heard by humans is 10-12 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.

Intensity Ratio Sound Intensity Ratio over threshold Threshold 10-12 W/m2 100 Whisper 10-10 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

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

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

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

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

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.

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.