The displacement of a particle at the position x = 0 in a medium due to two different progressive waves are `y_(1) = sin 4 pi t and y_(2) = sin 2 pi t` , respectively. How many times would the particle come to test in every second ?

Explanation

According to the principle of superposition, the resultant displacement of the particle is
` y = y_(1) + y_(2) = sin 4 pi t + sin 2 pi t `
`= 2 "sin" (4pi t + 2pi t)/(2) "cos"(4pi t - 2pi t)/(2) = 2 sin 3 pi t * cos pi t `
The particle comes to rest (y = 0) , when either sin ` 3 pi t = 0 or cos pi t = o `
When sin ` 3 pi t = 0 `, we have `t = 0 (1)/(3)s,(2)/(3)s " "(t lt 1 s)`
Again, when cos `pi t = 0 ` we have `t = (1)/(2)s" "(tlt1s)`
`:.` y = 0 , when ` t = 0 (1)/(3)s,(1)/(2)s,(2)/(3)s`
In every second, the particle comes to rest 4 times .