University Physics Volume 1

# Key Equations

### Key Equations

 Wave speed $v=λT=λfv=λT=λf$ Linear mass density $μ=mass of the stringlength of the stringμ=mass of the stringlength of the string$ Speed of a wave or pulse on a string undertension $|v|=FTμ|v|=FTμ$ Speed of a compression wave in a fluid $v=Βρv=Βρ$ Resultant wave from superposition of twosinusoidal waves that are identical except for aphase shift $yR(x,t)=[2Acos(ϕ2)]sin(kx−ωt+ϕ2)yR(x,t)=[2Acos(ϕ2)]sin(kx−ωt+ϕ2)$ Wave number $k≡2πλk≡2πλ$ Wave speed $v=ωkv=ωk$ A periodic wave $y(x,t)=Asin(kx∓ωt+ϕ)y(x,t)=Asin(kx∓ωt+ϕ)$ Phase of a wave $kx∓ωt+ϕkx∓ωt+ϕ$ The linear wave equation $∂2y(x,t)∂x2=1vw2∂2y(x,t)∂t2∂2y(x,t)∂x2=1vw2∂2y(x,t)∂t2$ Power averaged over a wavelength $Pave=EλT=12μA2ω2λT=12μA2ω2vPave=EλT=12μA2ω2λT=12μA2ω2v$ Intensity $I=PAI=PA$ Intensity for a spherical wave $I=P4πr2I=P4πr2$ Equation of a standing wave $y(x,t)=[2Asin(kx)]cos(ωt)y(x,t)=[2Asin(kx)]cos(ωt)$ Wavelength for symmetric boundaryconditions $λn=2nL,n=1,2,3,4,5...λn=2nL,n=1,2,3,4,5...$ Frequency for symmetric boundary conditions $fn=nv2L=nf1,n=1,2,3,4,5...fn=nv2L=nf1,n=1,2,3,4,5...$