First slide

Equation of wave

Question

A wave is represented by the equation $y = Asin (10 πx + 15 πt + π / 3)$ where x is in metre and t is in second. The expression represents

Moderate

A

a wave traveling in the positive x-direction with a velocity of.5m/s
B

a wave traveling in the negative x-direction with a velocity 1.5 m/s
C

a wave traveling in the negative x-detection with a wavelength of 0.2m
D

2 and 3 are correct

Solution

The equation of a plane wave moving in negative x-direction is given by
$y = Asin [\frac{2 π}{λ} (vt + x) + ϕ] Comparing the given equation with standard equation, we have \frac{2 π}{λ} = 10 π and \frac{2 π}{λ} v = 15 π ∴ λ = \frac{2}{10} = 0 \cdot 2 m and V = \frac{15 πλ}{2 π} = \frac{15 \times 0 \cdot 2}{2} = 1 \cdot 5 m / s Hence (2) and (3) are correct .$

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