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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 under
Speed of a compression wave in a fluid v=Βρv=Βρ
Resultant wave from superposition of two
sinusoidal waves that are identical except for a
phase shift
Wave number k2πλk2πλ
Wave speed v=ωkv=ωk
A periodic wave y(x,t)=Asin(kxωt+ϕ)y(x,t)=Asin(kxωt+ϕ)
Phase of a wave kxωt+ϕkxωt+ϕ
The linear wave equation 2y(x,t)x2=1vw22y(x,t)t22y(x,t)x2=1vw22y(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 boundary
Frequency for symmetric boundary conditions fn=nv2L=nf1,n=1,2,3,4,5...fn=nv2L=nf1,n=1,2,3,4,5...
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