Question

A wave is represented by the equation, y = A sin (10 πx + 15 πt + π/3) where x is in metre and t are in second. Which of the following statements is correct?

Options

• The wave is travelling in the direction of the negative X-axis with a speed of 1.5 ms^-1.

• The wave is travelling along the positive X-axis.

• The speed of the wave is 0.67 ms^-1.

• The wavelength of the wave is 5 m.

Answer 1

The wave is travelling in the direction of the negative X-axis with a speed of 1.5 ms^-1.

Explanation:

Comparing the given wave with

y = a sin(ωt - kx)

∴ 2πn = 15π ⇒ n = `15/2` ⇒ `(2pi)/lambda = 10pi` ⇒ λ = `1/5`

∴ v = nλ = `15/2 xx 1/5 = 3/2 = 1.5` m/s