Transverse wave are generated in two uniform steel wires A & B of same length but having diameters $$10$$−$$3m$$ and $$0.5$$×$$10$$−$$3m$$ respectively, by attaching their free end to a vibrating source of frequency $$500$$ Hz. Find the ratio of the wavelengths if they are stretched with the same tension.

Question

Transverse wave are generated in two uniform steel wires A & B of same length but having diameters  $$10$$−$$3m$$ and $$0.5$$×$$10$$−$$3m$$ respectively, by attaching their free end to a vibrating source of frequency $$500$$ Hz. Find the ratio of the wavelengths if they are stretched with the same tension.

Infinity Learn · Accepted Answer

Wave Speed  $$v=T$$μ ∴$$vAvB=$$μBμ$$A=dBdA$$   $${$$μ$$=Ml=$$π$$d2$$ρ$$4}$$ Also $$v=n$$λ ⇒v∝λ  Hence, we can say ∴$$vAvB=$$λAλ$$B=dBdA=0.5$$×$$10$$−$$310$$−$$3=0.5=12$$

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Transverse wave are generated in two uniform steel wires A & B of same length but having diameters 10−3m and 0.5×10−3m respectively, by attaching their free end to a vibrating source of frequency 500 Hz. Find the ratio of the wavelengths if they are stretched with the same tension.

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