Attenuation of Sound

Vortices on Sound Generation and Dissipation in Musical Flue Instruments

“…where c is the propagating sound velocity, η the dynamic viscosity, and ρ the air (or generally, gas) density. The coefficient α H due to heat conduction in gases is of the same order of magnitude as α F and is proportional to ω 2 [42]. The distance within which the sound level falls by 1 dB (an amplitude decrease of about 11%) due to classical absorption is very large in air (1-kHz wave gives 5 km; 10-kHz wave 50 m) [42].…”

“…velocity and temperature accompanying the acoustic wave [42]. As a result, the acoustic energy is removed from the acoustic wave.…”

“…A plane sound wave is exponentially damped in the direction of propagation (x direction): e Àαx . The coefficient α F of the dissipation due to internal friction is [42]…”

“…The major source of strong dissipation in free space is molecular sound absorption. The translational and rotational energies of gas molecule are very quickly increased by a sudden impact, while the oscillatory energy builds up gradually at the expense of the translational and rotational energies [42]. The delay in reaching thermal equilibrium is called relaxation, and its time constant is called the relaxation time τ R .…”

“…The relaxation frequency (defined as 1=2πτ R ) of pure oxygen is very low (about 10 Hz). However, the water vapor content of air greatly shortens the relaxation time and shifts the absorbing range into the audio frequencies (see Figure 3.7 in [42]). The acoustic dissipation in moist air is significantly greater than the classical absorption given by α F þ α H .…”