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Question
Answer in brief.
The amplitude of a wave is represented by y = 0.2 sin 4π `["t"/0.08-"x"/0.8]` in SI units. Find (a) wavelength, (b) frequency, and (c) amplitude of the wave.
Solution
Data: y = 0.2 sin 4π `["t"/0.08-"x"/0.8]`
y = 0.2 sin 2π `["2t"/0.08-"2x"/0.8]`
y = 0.2 sin 2π `["t"/0.04-"x"/0.4]`
Let us compare above equation with the equation of a simple harmonic progressive wave:
y = A sin 2π`["t"/"T"-"x"/λ]` = 0.2 sin 2π`["t"/0.04-"x"/0.4]`
Comparing the quantities on both sides, we get,
A = 0.2 m, T = 0.04 s, λ = 0.4 m
∴ (a) Wavelength (λ) = 0.4 m
(b) Frequency (n) = `1/"T"=1/0.04` = 25 Hz
(c) Amplitude (A)= 0.2 m
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