A wire of density $$9$$ × $$10-3$$ kg $$cm-3$$ is stretched between two clamps $$1m$$ apart. The resulting strain in the wire is $$4.9$$ × $$10-4$$. The lowest frequency of the transverse vibrations in the wire is (Young$$’s modulus of wire Y $$=$$ $$9$$ × $$1010$$ $$Nm-2), (to$$ the nearest $$integer), $$______$$

Question

A wire of density $$9$$ × $$10-3$$ kg $$cm-3$$ is stretched between two clamps $$1m$$ apart. The resulting strain in the wire is $$4.9$$ × $$10-4$$. The lowest frequency of the transverse vibrations in the wire is (Young$$’s modulus of wire Y $$=$$ $$9$$ × $$1010$$ $$Nm-2), (to$$ the nearest $$integer), $$______$$

Infinity Learn · Accepted Answer

Lowest frequency is fundamental $$frequencyf0=12lT$$μ              $$Y=TlA$$Δl​⇒$$f0=12lT$$ρA           $$TA=Y$$Δll⇒$$f0=12lY$$Δlρl​​Given :  $$l=1$$ ; Δ$$ll=4.9$$×$$10$$−$$4$$;  $$Y=9$$×$$1010$$ ;  ρ$$=9$$×$$10+3kgm3So$$ ​⇒$$f0=129$$×$$1010$$×$$4.9$$×$$10$$−$$49$$×$$103=124.9$$×$$103=1249$$×$$102=702=35$$ Hz

Stationary waves

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Stationary waves

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A wire of density 9 × 10-3 kg cm-3 is stretched between two clamps 1m apart. The resulting strain in the wire is 4.9 × 10-4. The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire Y = 9 × 1010 Nm-2), (to the nearest integer), ______

Lowest frequency is fundamental frequencyf0=12lTμ Y=TlAΔl​⇒f0=12lTρA TA=YΔll⇒f0=12lYΔlρl​​Given : l=1 ; Δll=4.9×10−4; Y=9×1010 ; ρ=9×10+3kgm3So ​⇒f0=129×1010×4.9×10−49×103=124.9×103=1249×102=702=35 Hz

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