The wave described by y = 0.25 sin (10 π x -2 πt), where x and y are in metre and t in second, is a wave travelling along the

- ve x direction with frequency 1 Hz

+ve x direction with frequency π Hz and wavelength λ = 0.2 m

+ve x direction with frequency 1 Hz and wavelength λ = 0.2 m

-ve x direction with amplitude 0.25 m and wavelength λ = 0.2 m

Solution

+ve x direction with frequency 1 Hz and wavelength λ = 0.2 m

The sign between two terms in the argument of sine will define its direction.
Writing the given wave equation
y= 0.25 sin (10 πx- 2πt) ... (i)
The minus (-) between (10πx) and (2πt) implies that the waves is travelling along the positive x-direction.
Now comparing eq (i) with standard wave equation
y = a sin (kx -ωt) ..... (ii)
we have
a= 0.25m, ω = 2π, k = 10 π m
therefore,
2π/T = 2π
f= 1Hz
λ = 2π/k = 2π/10π = 0.2 m
Therefore, the wave is travelling along +ve x direction wth frequency 1 Hz and wavelength 0.2m

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