Find beat frequency if the motion of two particles is given by y1=0.25sin (310 t) y2=0.25sin (316 t)

Question

Find beat frequency if the motion of two particles is given by y1=0.25sin (310 t) y2=0.25sin (316 t) (A) 3 (B) (3/π ) (C) (6/π ) (D) 6

Tardigrade Admin · Accepted Answer

The given equations of waves be written as

y_{1} = 0.25 s in (310 t) \dots (i)

And

y_{2} = 0.25 s in (316 t) \dots (ii)

Comparing Eqs. (i) and (ii) with the standard wave equation, written as

y = a s in (ω t) \dots (iii)

We have,

ω_{1} = 310

⟹ v_{1} = \frac{310}{2 π} u ni t

And

ω_{2} = 316

⟹ v_{2} = \frac{316}{2 π} u ni t

Hence, beat frequency=

v_{2} - v_{1}

= \frac{316}{2 π} - \frac{310}{2 π} = \frac{3}{π} u ni t

Q. Find beat frequency if the motion of two particles is given by

$y_{1} = 0.25 s in (310 t)$

$y_{2} = 0.25 s in (316 t)$