The transverse displacement of a string clamped at its both ends is given by $$y(x$$,$$t)=0.06sin$$⁡$$2$$$$π$$$$3xcos$$⁡(120$$$$π$$$$t) where x and y are in m and t in s. The length of the string is $$1.5$$ m and its mass is $$3$$×$$10$$−$$2kg$$. The tension in the string is

Question

The transverse displacement of a string clamped at its both ends is given by $$y(x$$,$$t)=0.06sin$$⁡$$2$$$$π$$$$3xcos$$⁡(120$$$$π$$$$t) where x and y are in m and t in s. The length of the string is $$1.5$$ m and its mass is $$3$$×$$10$$−$$2kg$$. The tension in the string is

Infinity Learn · Accepted Answer

The given equation $$isy(x$$,$$t)=0.06sin$$⁡$$2$$$$π$$$$3xcos$$⁡$$(120$$$$π$$$$t)Compare$$ it with $$y(x$$,$$t)=2asin$$⁡kxcos⁡ωtwe get, $$k=2$$$$π$$$$3$$,  or  $$2$$πλ$$=2$$$$π$$$$3$$  or  λ$$=3mand$$ ω$$=120$$π or $$2$$$$π$$$$v=120$$π or $$v=60Hz=60s$$−$$1Velocity$$ of wave, $$v=v$$λ$$=60s$$−$$1(3m)=180ms$$−$$1Mass$$ per unit length of the string,μ$$=3$$×$$10$$−$$2kg1.5m=2$$×$$10$$−$$2kgm$$−$$1Velocity$$ of transverse wave in the string, $$v=T$$μ or $$v2=T$$μ or $$T=v2$$μ$$T=180ms$$−$$122$$×$$10$$−$$2kgm$$−$$1=648N$$

The transverse displacement of a string clamped at its both ends is given by $y (x, t) = 0 .06 \sin (\frac{2 π}{3} x) \cos (120 πt)$ where x and y are in m and t in s. The length of the string is 1.5 m and its mass is $3 \times 10^{- 2} kg$ . The tension in the string is

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The transverse displacement of a string clamped at its both ends is given by y(x,t)=0.06sin⁡2π3xcos⁡(120πt) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3×10−2kg. The tension in the string is

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The transverse displacement of a string clamped at its both ends is given by $y (x, t) = 0 .06 \sin (\frac{2 π}{3} x) \cos (120 πt)$ where x and y are in m and t in s. The length of the string is 1.5 m and its mass is $3 \times 10^{- 2} kg$ . The tension in the string is