The equation of a certain progressive transverse wave is y = 2 sin 2 \(\pi ( \frac{t}{0.01} - \frac{x}{30})\), where x and y are in cm and t in seconds. Cal...
Question 1 Report
The equation of a certain progressive transverse wave is y = 2 sin 2 \(\pi ( \frac{t}{0.01} - \frac{x}{30})\), where x and y are in cm and t in seconds. Calculate the period of the wave.
Answer Details
The general equation of a progressive transverse wave is given by:
y = A sin (kx - ωt)
where A is the amplitude, k is the wave number, x is the position of the particle, ω is the angular frequency, and t is the time.
Comparing this equation with the given equation, we have:
A = 2 cm
k = 2π/30 cm^(-1) = π/15 cm^(-1)
ω = 2π/T, where T is the period
Thus, we have:
ω = 2π/T = 2π/(0.01 s)
Substituting the value of ω, we get:
2π/(0.01 s) = π/15 cm^(-1)
Simplifying this equation, we get:
T = 0.01 s
Therefore, the period of the wave is 0.01 s.
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