A sonometer wire of length $$1.5m$$ is made of steel. The tension in it produce an elastic strain of $$1$$%. What is the fundamental frequency of transverse vibrations in Hz if density and young’s modulus of steel are $$7.7$$×$$103$$ $$kg/m3$$ and $$15.4$$×$$1011$$ $$N/m2$$ respectively? $$2=1.414$$,$$3=1.732$$,$$5=2.236$$

Question

A sonometer wire of length $$1.5m$$ is made of steel. The tension in it produce an elastic strain of $$1$$%. What is the fundamental frequency of transverse vibrations in Hz if density and young’s modulus of steel are  $$7.7$$×$$103$$ $$kg/m3$$ and $$15.4$$×$$1011$$ $$N/m2$$ respectively? $$2=1.414$$,$$3=1.732$$,$$5=2.236$$

Infinity Learn · Accepted Answer

Given length of wire  $$l=1.5$$ mYoung’s modulus  $$Y=stressstrain=15.4$$×$$1011$$ $$N/m2Stress=Tension/Cross$$ section area $$=$$ $$TAStrain=1$$%$$=0.01$$⇒$$15.4$$×$$1011=T/A0.01$$⇒$$15.4$$×$$1011=T0.01A$$⇒$$T=15.4$$×$$109$$×A Volume density  $$d=7.7$$×$$103$$ $$kg/m3Linear$$ density  μ$$=Volume$$ density×$$Area=d$$×A      $$=7.7$$×$$103$$×A      Velocity of transverse wave on the sonometer wire $$V=T$$μ⇒$$V=15.4$$×$$1097.7$$×$$103$$ $$=2$$×$$103m/s$$ Fundamental note has a wave length  λ$$=2L=3$$ mSo, $$frequency=$$ Vλ$$=2$$×$$1033=471.33Hz$$.

Stationary waves

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A sonometer wire of length 1.5m is made of steel. The tension in it produce an elastic strain of 1%. What is the fundamental frequency of transverse vibrations in Hz if density and young’s modulus of steel are 7.7×103 kg/m3 and 15.4×1011 N/m2 respectively? 2=1.414,3=1.732,5=2.236

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