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Question
The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25). Where all quantities are in the S.I. system. Find the amplitude, frequency, wavelength, and velocity of the wave.
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Solution
- Given equation:
y = sin`pi/2((4"t")/0.025 - "x"/0.25)`
y = sin`((2pi"t")/0.025 - (pi"x")/0.5)`
Comparing above equation with y = A sin`(ω"t" - (2pi"x")/λ)`
∴ A = 1 m - ω = `(2pi)/0.025`
∴ 2πn = `(2pi)/0.025`
∴ n = 40 Hz - `(2pi)/λ = pi/0.5`
∴ λ = 1 m - v = nλ
= 40 × 1
= 40 m/s
The amplitude, frequency, wavelength, and velocity of the wave are 1 m, 40 Hz, 1 m, and 40 m/s respectively.
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