Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is ‘a’ and the phase of A is ahead by π$$3$$ than that of B and the distance AP is greater than BP by $$50$$ cm. Then the resultant amplitude at the point P will be, if the wavelength is $$1$$ meter

Question

Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is ‘a’ and the phase of A is ahead by π$$3$$ than that of B and the distance AP is greater than BP by $$50$$ cm. Then the resultant amplitude at the point P will be, if the wavelength is $$1$$ meter

Infinity Learn · Accepted Answer

Path difference $$($$Δ$$x)=50$$ cm $$=12m$$∴ Phase difference Δφ$$=2$$πλ×Δx⇒φ$$=2$$$$π$$$$1$$×$$12=$$π Total phase difference $$=$$  π−π$$3=2$$$$π$$$$3$$⇒$$A=a2+a2+2a2cos(2$$π$$/3)=a$$

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