Question

A transverse wave is described by the equation, y = Y₀ sin 2π(ft - `"x"/lambda`). The maximum particle velocity is equal to four times the wave velocity if ______

Options

• `lambda = (piy_0)/4`

• `lambda = (piy_0)/2`

• `lambda = piy_0`

• `lambda = 2piy_0`

Answer 1

A transverse wave is described by the equation, y = Y₀ sin 2π(ft - `"x"/lambda`). The maximum particle velocity is equal to four times the wave velocity if `underline(lambda = (piy_0)/2)`.

Explanation:

y = Y₀ sin 2π`("ft" - "x"/lambda)`

∴ `"dy"/"dt" = "y"_0 2pi"f" cos2pi("ft" - "x"/lambda)`

∴ `|"dy"/"dt"|_"max" = y_0 2pi"f"`

∵ Wave velocity= fλ

According to the given condition, `y_0 2pi"f" = 4"f"lambda`

∴ `lambda = (piy_0)/2`