- #1
LizardCobra
- 17
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What is [an] equation for a transverse wave with no boundary conditions, as a function of x and t? I want to model a fluctuation string where neither of the ends are bound.
Post#3
Would y=Acos(kx-wt) + Bcos(kx+wt) + Csin(kx-wt) + Dsin(kx+wt)
Post#6
y = Ʃ sin(nπx/L)*[An cos(ωt) + Bn sin(ωt] + cos(nπx/L)*[Cn cos(ωt) + Dn sin(ωt].
Post#8
I've modeled the shape at t = 0 as Ʃ Asin(nπx/L) +Bcos(nπx/L). Can I just multiply this by (cos(wt) + sin(wt)) to make it a function of time?
You can use "periodic boundary conditions".LizardCobra said:What is [an] equation for a transverse wave with no boundary conditions, as a function of x and t? I want to model a fluctuation string where neither of the ends are bound.
The equation for a transverse wave is given by: y(x,t) = A*sin(kx - ωt + ϕ), where A is the amplitude, k is the wave number, ω is the angular frequency, x is the position, t is the time, and ϕ is the phase constant.
The amplitude (A) represents the maximum displacement of the wave from its equilibrium position. The wave number (k) represents the number of complete wave cycles per unit distance. The angular frequency (ω) represents the number of complete wave cycles per unit time. The position (x) and time (t) are variables that determine the location and time of the wave. The phase constant (ϕ) represents the initial phase of the wave.
The equation for a transverse wave includes the sine function, whereas the equation for a longitudinal wave includes the cosine function. This is because transverse waves oscillate perpendicular to the direction of propagation, while longitudinal waves oscillate parallel to the direction of propagation.
No, the equation for a transverse wave is specific to transverse waves only. Different types of waves, such as longitudinal waves and surface waves, have their own unique equations that describe their behavior.
The equation for a transverse wave is used in various fields of science and engineering, such as acoustics, optics, and electromagnetism. It is used to model and analyze the behavior of different types of transverse waves, such as light, sound, and electromagnetic waves. It is also used in the design and development of technologies that utilize transverse waves, such as antennas, lasers, and musical instruments.