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Question

derive the equations for harmonic frequencies of standing waves formed in a string due to the superposition of waves.Draw the first two harmonies

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Solution

Dear studentLength of string= L Velocity of wave on string =Va)when wire vibrate forming one loop or first harmonic L=λ2 so λ=2LV=f1×λ=f1×2Lf1=V2L...1b)when wire vibrate in two loops or second harmonicL=2λ2 so λ=LV=f2×λ=f2×Lf2=VL...2c)when wire vibrate in three loops or third harmonicL=3λ2 so λ=2L3V=f3×λ=f3×2L3f3=3V2L=3f1...3when wire vibrate forming n loops or nth harmonic thanL=nλ2 so λ=2LnV=fn×λ=fn×2Lnfn=V2Ln=nV2L=nf1...(n)Regards

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