Approximately how does the density of air vary with altitude

Section 17­19 notes Wave Motion is characterized by  Reflection – bouncing back when there is an abrupt change in medium  Refraction – waves travel faster when going through a medium  Diffraction – bending of the wave around obstacles  Doppler Shift – change in frequency due to relative motion between source and receiver  Beats – a modulation in time of intensity  Interference – spatial modulation of intensity due to coherent addition Specular Reflection – reflection from a smooth surface Diffuse Reflection – reflection from a rough surface In gases, as density increases, the sound decreases, and vice­versa. Hoygen's principle: every point on the wave is the source of a new (spherical) wavelet. Diffraction helps you hear things around the corner. R=10log(3+((40fd)/v)) R = the reduction (dB) over the f = the frequency (Hz), d = the path difference between diffracted and direct sounds, and v = the speed of sound (usually 343 m/s). Doppler Effect – the apparent change of the frequency of a wave based on the movement between the wave's source and the observer. Addition of waves – when 2 tones are added, the amplitudes are added. I(coherent) = (A1 + A2)^2 When the tones are outside the critical bandwidth, I(incoherent) = A1^2 + A2^2 Beats – a modulation in time of intensity Interference – the coherent addition of waves at various points in space that leads to modulation of the intensity in space. Superposition – When 2 waves interfere, the displacement is the algebraic sum of the waves. Beat Frequency f(mean) = (f1