 ### Sound

1. Intensity is defined as power per unit area.
2. Using the reference intensity I0 ≡ 10-12 W/m2, we define the sound level in decibels as
db ≡ 10 log(I / I0).
3. For a sound source approaching an observer at speed uS, the observed wavelength is shortened by the source translation distance in one period:
λO = λS - uS TS
or, with TS = λS / c:
λO = λS (c - uS) / c
4. If the observer is approaching the source at speed uO, the observed wavelength is shortened by the observer translation distance in one period as observed by the observer:
λO = λS - uO TO
or, with TO = λO / c:
λO = λS c / (c + uO)
5. Putting these together, we have the general equation for the one-dimensional Doppler Effect: the shift in observed wavelength as a function of the velocities of the source and observer:
λO = λS (c - uS) / (c + uO)
or, in terms of frequency:
νO = νS (c + uO) / (c - uS)
Note that if the source is moving away from the observer, uS < 0. Likewise, if the observer is moving away from the source, uO < 0.
6. For sound waves in air:
c = √ (γ R T / M),
where (as we will later find), γ is 1.4 for air (whose molecules are assumed to be diatomic), R is the molar gas constant, T is the temperature in Kelvin and M is the molar mass (0.02895 kg/mole for air). This equation approximates to
c = 20.05 m/s * √ T

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