A large tank is filled with pure nitrogen at rest at a temperature of K

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

Fluids and Continuum Physics, Ch Acoustics: sound propagation, radiation and attenuation

Problem

A large tank is filled with pure nitrogen at rest at a temperature of 288288 K. The nitrogen is treated as an ideal gas with ratio of specific heats κ=1.40\kappa = 1.40 and molar mass M=0.0280M = 0.0280 kg mol−1^{-1}; its rest density is ρ0=1.17\rho_0 = 1.17 kg m−3^{-3}. The molar gas constant is R=8.314R = 8.314 J mol−1^{-1} K−1^{-1}. A loudspeaker sends a plane sound wave travelling in one direction through the gas; the wave is small in amplitude and losses are ignored. ((a)) Find the speed of sound in the nitrogen. ((b)) The wave has a root-mean-square acoustic pressure prms=0.50p_{\rm rms} = 0.50 Pa. Find its intensity. ((c)) Express that intensity as a sound level in decibels, using the reference intensity I0=1.0×10−12I_0 = 1.0\times10^{-12} W m−2^{-2}.

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