Someone evaluates the classical absorption formula for air at and concludes that a…

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Acoustics of fluids: generation, propagation and attenuation · Acoustics of fluids: generation, propagation and attenuation

Signal Speeds in Fluids, Ch Sound in a moving, absorbing fluid: sources, refraction and loss

Problem

Someone evaluates the classical absorption formula for air at

20^\circ\mathrm{C}

and concludes that a

4\,\mathrm{kHz}

alarm loses only about

25\,\mathrm{dB}

over

10\,\mathrm{km}

. Take

\mu=1.81\times10^{-5}\,\mathrm{Pa\,s}

\mu_{\rm b}=0.6\mu

k_T=0.0257\,\mathrm{W\,m^{-1}\,K^{-1}}

\gamma=1.4

c_p=1005\,\mathrm{J\,kg^{-1}\,K^{-1}}

\rho_0=1.204\,\mathrm{kg\,m^{-3}}

and

c_0=343.2\,\mathrm{m\,s^{-1}}

. ((a)) Evaluate the classical

\alpha

4\,\mathrm{kHz}

\mathrm{Np\,m^{-1}}

and in

\mathrm{dB\,km^{-1}}

, and confirm the

25\,\mathrm{dB}

. ((b)) The measured absorption at

4\,\mathrm{kHz}

and

50

per cent relative humidity is about

30\,\mathrm{dB\,km^{-1}}

. What does the classical formula leave out, and what is the real loss over

10\,\mathrm{km}

? ((c)) For water at

3\,\mathrm{MHz}

(

\rho_0=998\,\mathrm{kg\,m^{-3}}

c_0=1482\,\mathrm{m\,s^{-1}}

\mu=1.0\times10^{-3}\,\mathrm{Pa\,s}

\mu_{\rm b}=2.8\times10^{-3}\,\mathrm{Pa\,s}

, conduction negligible), evaluate

\alpha

and the distance over which a beam's intensity halves.

Browse the problem library