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University Physics Volume 1

# Key Equations

### Key Equations

 Pressure of a sound wave $ΔP=ΔPmaxsin(kx∓ωt+ϕ)ΔP=ΔPmaxsin(kx∓ωt+ϕ)$ Displacement of the oscillating molecules of asound wave $s(x,t)=smaxcos(kx∓ωt+ϕ)s(x,t)=smaxcos(kx∓ωt+ϕ)$ Velocity of a wave $v=fλv=fλ$ Speed of sound in a fluid $v=βρv=βρ$ Speed of sound in a solid $v=Yρv=Yρ$ Speed of sound in an ideal gas $v=γRTMv=γRTM$ Speed of sound in air as a function of temperature $v=331msTK273K=331ms1+TC273°Cv=331msTK273K=331ms1+TC273°C$ Decrease in intensity as a spherical wave expands $I2=I1(r1r2)2I2=I1(r1r2)2$ Intensity averaged over a period $I=〈 P 〉AI=〈 P 〉A$ Intensity of sound $I=(Δpmax)22ρvI=(Δpmax)22ρv$ Sound intensity level $β(dB)=10log10(II0)β(dB)=10log10(II0)$ Resonant wavelengths of a tube closed at one end $λn=4nL,n=1,3,5,…λn=4nL,n=1,3,5,…$ Resonant frequencies of a tube closed at one end $fn=nv4L,n=1,3,5,…fn=nv4L,n=1,3,5,…$ Resonant wavelengths of a tube open at both ends $λn=2nL,n=1,2,3,…λn=2nL,n=1,2,3,…$ Resonant frequencies of a tube open at both ends $fn=nv2L,n=1,2,3,…fn=nv2L,n=1,2,3,…$ Beat frequency produced by two waves thatdiffer in frequency $fbeat=|f2−f1|fbeat=|f2−f1|$ Observed frequency for a stationary observerand a moving source $fo=fs(vv∓vs)fo=fs(vv∓vs)$ Observed frequency for a moving observerand a stationary source $fo=fs(v±vov)fo=fs(v±vov)$ Doppler shift for the observed frequency $fo=fs(v±vov∓vs)fo=fs(v±vov∓vs)$ Mach number $M=vsvM=vsv$ Sine of angle formed by shock wave $sinθ=vvs=1Msinθ=vvs=1M$
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