Two vibrating tuning forks produce progressive waves given by y, `y _(1) = 4 sin 500 pi t and y _(2) = 2 sin 506 pi t.` Number of beats produced per minute is ......

Options

A. 360
B. 180
C. 60
D. 3

Answer

B

Explanation

We have `y _(1) = 4 sin (500pi t ) = 4 sin (2pi f _(1) t )`
`implies 2pi f _(1) = 500 pi implies f_(1) = 250 Hz`
Also `y _(2) = 2 sin (506 pi t ) = 2 sin (2pi f _(2) t )`
`implies 2pi f _(2) = 506 pi implies f_(2) = 253 Hz`
Beat frequency,` f _(2) - f_(1) =253 -250 =3 Hz`
`therefore f _(2) -f _(1)` =3 beat /second
`= 3 ("beat")/((1)/(60) "minute")`
`= 3 xx 60` beat/minute
`=180 ` beat/minute