Two harmonic waves moving in the same direction superimpose to form a wave x = a cos ( 1.5 t ) cos ( 50.5 t ) where t is in seconds. Find the period with which they beat (close to nearest integer)

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The given equation can be written as x = 2 a ​ cos [ 1.5 + 50.5 ] t + 2 a ​ cos [ 50.5 − 1.5 ] x = 2 a ​ cos [ 52 t ] + 2 a ​ cos [ 49 t ] Here, 2 π f 1 ​ &2 π f 2 ​ = 49 f 1 ​ = 2 π 52 ​ , f 2 ​ = 2 π 49 ​ ∴ f Bat ​ = f 1 ​ − f 2 ​ = 2 π 3 ​ Hz ∴ T Beat ​ = f Beat ​ 1 ​ = 3 2 π ​ sec = 2.09 sec ≈ 2 sec

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