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Question
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is ______.
Options
2 m/s
150 m/s
200 m/s
300 m/s
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Solution
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is 300 m/s.
Explanation:
y = 5cos`[200pit - pi/150x]`
y = Acos(ωt - Kx)
A = 5 cm
ω = 200π
2πf = 200π = 100 Hz
K = `pi/150 = (2pi)/lambda`
λ = 300 cm
V = fλ = `100 xx 300 xx 10^-2 = 300` m/s
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