A travelling wave on a string is given by $$y=7.5sin(0.005x+12t+$$π$$/4)$$ . Find the displacement and velocity of the particle at a point $$x=1$$ cm $$t=1sec$$ . Take $$sin$$$$(12.7o)=0.22$$ .

Question

A travelling wave on a string is given by $$y=7.5sin(0.005x+12t+$$π$$/4)$$ . Find the displacement and velocity of the particle at a point $$x=1$$ cm  $$t=1sec$$  . Take $$sin$$$$(12.7o)=0.22$$  .

Infinity Learn · Accepted Answer

Given  $$y=7.5sin0.005x+12t+$$π$$/4$$→(i) Putting $$x=1cm$$  and $$t=1sec$$ in eq (i) we have $$y=7.5sin0.005$$×$$1+12$$×$$1+3.1424$$ $$=7.5sin12.79$$ rad $$=7.5sin732.70$$      π $$rad=1800$$ $$=7.5sin4$$π$$+12.70$$ $$=7.5sin12.70$$ $$=7.5$$×$$0.22=1.65$$​cm  Particle velocity is obtained by differentiating (i) w.r.t time t $$v=dy/dt=7.5$$×$$12$$×$$cos0.005x+12t+$$π$$/4$$  Putting $$x=1cm$$ and  $$t=1sec$$ $$v=7.5$$×$$12$$×$$cos$$$$(12.70)=87.8$$ $$cm/$$$$sec$$

A travelling wave on a string is given by $y = 7.5 \sin (0.005 x + 12 t + π / 4)$ . Find the displacement and velocity of the particle at a point $x = 1 c m$ $t = 1 \sec$ . Take $[\sin ({12.7}^{o}) = 0.22]$ .

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A travelling wave on a string is given by y=7.5sin(0.005x+12t+π/4) . Find the displacement and velocity of the particle at a point x=1 cm t=1sec . Take sin(12.7o)=0.22 .

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A travelling wave on a string is given by $y = 7.5 \sin (0.005 x + 12 t + π / 4)$ . Find the displacement and velocity of the particle at a point $x = 1 c m$ $t = 1 \sec$ . Take $[\sin ({12.7}^{o}) = 0.22]$ .