Question

Two waves Y₁ = 0.25 sin 316 t and Y₂ = 0.25 sin 310 t are propagating along the same direction. The number of beats produced per second are ______.

Options

• `pi/2`

• `2/pi`

• `3/pi`

• `pi/3`

Answer 1

Two waves Y₁ = 0.25 sin 316 t and Y₂ = 0.25 sin 310 t are propagating along the same direction. The number of beats produced per second is `3/pi`.

Explanation:

Given, y₁ = 0.25 sin 316 t

and y₂ = 0.25 sin 310 t

Comparing with tile standard equation,

y = A sin ωt

we get

`omega_1 = 316 " rad"//"s"=>2pi"f"_1=316  "or"  "f"_1=316/(2pi)"Hz"`

and `omega_2 = 310 " rad"//"s"=>2pi"f"_2=310  "or"  "f"_2=310/(2pi)"Hz"`

∴ Beat frequency or number of beats produced per second

`= "f"_1-"f"_2=(316-310)/(2pi)=6/(2pi)=3/pi`