Question

If y = y₀ sin 2π `("ft" - x/lambda)` is, the equation of transverse wave, then for what value of λ the maximum particle velocity is equal to four times the wave velocity?

Options

• y₀π

• `("y"_0pi)/2`

• 2y₀π

• 15y₀π

Answer 1

`underlinebb(("y"_0pi)/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`