Atmospheric Acoustic Remote Sensing - Chapter 3 ppt

3 Sound in the Atmosphere Acoustic remote-sensing tools use the interaction between sound and the atmosphere to yield information about the state of the atmospheric boundary layer SODAR (SOund Detection And Ranging) and RASS (Radio Acoustic Sounding System) use vertical propagation of sound to give vertical profiles of important properties, whereas acoustic tomography uses horizontal propagation of sound to visualize the boundary layer structure in a horizontal plane In Chapter 2, some of the fundamental properties of the turbulent boundary layer were discussed In this chapter, the properties of sound are outlined For a general coverage, see Salomons (2001) The primary interest here is what happens to the energy in a narrow acoustic beam directed into the atmosphere In this case, the main effects are: spreading of the sound over a larger area as it gets further from the source; atmospheric absorption; sound propagation speed; bending of the beam due to refraction; scattering from turbulence; and Doppler shift of the received sound frequency Discussion of diffraction over acoustic shielding and the reflection from hard surfaces will be left to a later chapter 3.1 BASICS OF SOUND WAVES When the flexible diaphragm of a speaker moves, it creates small pressure fluctuations traveling outward from the speaker These pressure fluctuations are sound waves The speed, c, at which these waves travel can be expected to depend on the mechanical properties patm (atmospheric pressure) and (air density) A dimensional analysis, similar to those in Chapter 2, shows that patm c (3.1) and, as already noted, the temperature and density are inversely related to each other at constant pressure through the gas equation patm Rd T , where Rd = 287 J kg–1 K–1 This means that c T (3.2) Allowing for T being the temperature in K, and that the speed of sound at 0°C is 332 m s–1, c (T ) 332 (1 0.00166 T ) m s 1, (3.3) 27 © 2008 by Taylor & Francis Group, LLC 3588_C003.indd 27 11/20/07 4:37:13 PM 28 Atmospheric Acoustic Remote Sensing where ∆T is the temperature in °C For air containing water vapor, the air density is the sum of the dry air density, d, and the water vapor density, v, or d patm pv Rd T v pv , ( Rd / )T where = 0.622 is the ratio of the molecular weight of water to molecular weight of air, and individual gas equations have been used for dry air and for water vapor A simpler expression is obtained in terms of the water vapor mixing ratio, w pv / ( patm pv ) , which is the mass of water vapor divided by the mass of dry air per unit volume Rearranging gives patm Rd w/ T w Rd Tv , where Tv, the virtual temperature, allows for the slight decrease in density of moist air More precisely, the adiabatic sound speed is RT c , M where R = 8.31 J mol–1 K–1 is a universal gas constant, is the ratio of specific heats for the gas, and M is the average molecular weight This sound speed does not allow for the effect of air motion (i.e., wind) in changing the speed along the direction of propagation When a fraction h = pv/patm of the molecules is water vapor, both and M depend on h via h , h M M dry air (1 h ) hM water These expressions interpolate between dry air = 7/5 and water = 8/6, and also between the two molecular weights After a little algebra, and allowing for the fact that h> , R r2 R R 2r r sin cos( ) and, if the antenna gain is uniform across the antenna, p A e j( r a t kr ) e jk sin cos( ) d( ) d , © 2008 by Taylor & Francis Group, LLC 3588_C003.indd 36 11/20/07 4:37:57 PM Sound in the Atmosphere 39 λ u uTD cTD c c cTD λD FIGURE 3.8 Reflection of sound from a target moving in the direction of sound propagation The dashed lines show positions of reflected pressure maxima at a time TD after the first pressure maximum reaches the target patch and in the opposite direction X tupwind dx c( x) u( x ) (3.22) , where both wind speed and sound speed can, in general, vary along the path These times are identical for successive pressure maxima so there is no Doppler shift However, the downwind and upwind travel times can distinguish temperature variations (changes in c) from wind speed variations (changes in u) since u