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The wave described by y = 0.25 sin (10πx − 2πt), where x and y are in meters and t in seconds, is a wave travelling along the:

1. −x direction with frequency 1 Hz.
2. +x direction with frequency π Hz and wavelength λ = 0.2 m.
3. +x direction with frequency 1 Hz and wavelength λ = 0.2 m.
4. −x direction with amplitude 0.25 m and wavelength λ = 0.2 m.

Correct answer: +x direction with frequency 1 Hz and wavelength λ = 0.2 m.

Solution

The wave equation y = 0.25 sin(10πx − 2πt) has the form y = A sin(kx − ωt), indicating a wave traveling in the +x direction. The angular frequency ω = 2π rad/s gives a frequency f = ω/2π = 1 Hz, and the wave number k = 10π rad/m gives a wavelength λ = 2π/k = 0.2 m.

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