STANDARD Physics Progressive Waves Multiple Correct Question
The equation of a progressive wave is given by: y = 5 sin(100 πt − 0.4πx) where y and x are in m and t is in s. (1) The amplitude of the wave is 5 m. (2) The wavelength of the wave is 5 m. (3) The frequency of the wave is 50 Hz. (4) The velocity of the wave is 250 m s⁻¹. Which of the following statements are correct?
(1), (2) and (3)
(2) and (3)
(1) and (4)
All are correct
Correct Answer
Detailed Explanation
The equation of a given progressive wave is y = 5 sin(100πt − 0.4πx). Comparing with the standard equation y = a sin(ωt − kx), we find a = 5m, ω = 100π rad s⁻¹, k = 0.4π m⁻¹. The amplitude is 5 m, wavelength λ = 2π/k = 5 m, frequency f = ω/2π = 50 Hz, and velocity v = ω/k = 250 m s⁻¹.
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