A string of length $$1m$$ has the mass per unit length $$0.1$$ $$gm/cm$$ . Two ends of the string are attached to two rigid walls. A transverse vibration is set up in the string . A tension of $$400$$ N is maintained in the string $$2t$$ the string oscillates in the first overtone and maximum displacement of a particle of the string is $$2mm$$, the maximum velocity of a particle of the string is

Question

A string of length $$1m$$ has the mass per unit length $$0.1$$ $$gm/cm$$ . Two ends of the string are attached to two rigid walls. A transverse vibration is set up in the string . A tension of $$400$$ N is maintained in the string $$2t$$ the string oscillates in the first overtone and maximum displacement of a particle of the string is $$2mm$$, the maximum velocity of a particle of the string is

Infinity Learn · Accepted Answer

$$2$$×λ$$2=l$$⇒λ$$=l=1mVelocity$$ of wave, $$v=T$$μ$$=40010$$−$$2m/s=200$$ $$m/s$$∴Frequency, $$f=v$$λ$$=2001Hz=200Hz$$∴Maximum particle velocity, $$umax=A$$×$$2$$$$π$$$$f=2$$×$$10$$−$$3$$×$$2$$π×$$200m/s$$                                                                                                                             $$=2.512m/s$$

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