The equation of displacement of two waves are given as $$y1=10sin3$$$$π$$$$t+$$π$$3$$; $$y2=5(sin3$$$$π$$$$t+3cos3$$$$π$$$$t)$$. Then what is the ratio of their amplitudes

Question

The equation of displacement of two waves are given as $$y1=10sin3$$$$π$$$$t+$$π$$3$$; $$y2=5(sin3$$$$π$$$$t+3cos3$$$$π$$$$t)$$. Then what is the ratio of their amplitudes

Infinity Learn · Accepted Answer

$$y1=10sin$$ $$3$$$$π$$$$t+$$π$$3$$                   ...(i)and$$ $$y2=5$$[$$sin3$$$$π$$$$t+3cos$$ $$3$$$$π$$t]$$=5$$×$$2$$ $$12$$×$$sin3$$$$π$$$$t+32$$×$$cos3$$$$π$$$$t=10$$ $$cos$$$$π$$$$3sin3$$$$π$$$$t+$$$$sin$$$$π$$$$3cos$$$$π$$$$t=10$$ $$sin$$ $$3$$$$π$$$$t+$$πt                ... $$(ii)                                   $$($$∵ $$sin$$(A$$ $$+$$ $$B) $$=$$ sinA cosB $$+$$ cosA $$sinB)Comparing$$ equation (i) and (ii) we get ratio of amplitude $$1$$ : $$1$$.

The equation of displacement of two waves are given as $y_{1} = 10 \sin (3 πt + \frac{π}{3})$ ; $y_{2} = 5 (\sin 3 πt + \sqrt{3} \cos 3 πt)$ . Then what is the ratio of their amplitudes

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The equation of displacement of two waves are given as y1=10sin3πt+π3; y2=5(sin3πt+3cos3πt). Then what is the ratio of their amplitudes

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The equation of displacement of two waves are given as $y_{1} = 10 \sin (3 πt + \frac{π}{3})$ ; $y_{2} = 5 (\sin 3 πt + \sqrt{3} \cos 3 πt)$ . Then what is the ratio of their amplitudes