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The transverse displacement (y) of a wave is given as a function of position...?
Consider the waveform expression.
Y (x,t) = ymSin(1.73 + 0.435x +531t)
The transverse displacement (y) of a wave is given as a function of position (x in meters) and time (t in seconds) by the expression. Determine the wavelength, frequency, period, and phase constant of this waveform.
λ = ? Metres
T= ? Seconds
f = ? Hertz
ϕ = ? Radians
1 Answer
- anonymousLv 71 year agoFavorite Answer
I'll note that I'm more of a math person than a physics person, but I'm trying to get up to speed on wave equations (hence no guarantees). Here's what I got after reviewing transverse waves.
transverse wave equation:
y(x, t) = A sin(kx ∓ ωt + 𝜙)
amplitude: A
wave number: k = 2π/λ
angular frequency: ω = 2π/T
velocity: v = ω/k
phase shift: 𝜙
wavelength: λ = 2π/k
period: T = 2π/ω
frequency: f =1/T
----
Y(x,t) = ym sin(1.73 + 0.435x + 531t)
Comparing the transverse wave equation to the expression in the question,
k = 0.435 m⁻¹
ω = 531 s⁻¹
𝜙 = 1.73 radians
so
wavelength: λ = 2π/k = (2π / 0.435 m⁻¹) = 14.4 m
period: T = 2π/ω = (2π / 531 s⁻¹) = 0.0118 s
frequency: f = 1/T = (1 / 0.0118 s) = 84.7 s⁻¹
phase constant: 𝜙 = 1.73 radians