a), Just pop 0 into the equation, what are you left with?
b) ω is 2pi/T, so pop that into the equation.
c) ?? Not sure. I think it's whenever Sin(wt) = 0, so 0, pi, 2pi, 3pi etc.
But I think wavelenth is 2pi, so 1/2, 1, 3/2 might be the answer.
Hi, can anybody provide some hints in how to approach these questions? I've been stuck on it for days!!! Thank you in advance!!
Nodes of a Standing Wave:
Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave:
y(x,t)=Acos(kx)sin(ωt),
where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, ω is the angular frequency of the wave, and t is time.
a) At time t=0, what is the displacement of the string y(x,0)?
Express your answer in terms of A, k, and other previously introduced quantities.
b)What is the displacement of the string as a function of x at time T/4, where T is the period of oscillation of the string?
Express the displacement in terms of A, x, and k only. That is, evaluate ω⋅T4 and substitute it in the equation for y(x,t).
c)At which three points x1, x2, and x3 closest to x=0 but with x>0 will the displacement of the string y(x,t) be zero for all times? These are the first three nodal points.
Express the first three nonzero nodal points as multiples of the wavelength λ, using constants like π. List the factors that multiply λ in increasing order, separated by commas.
3 answers
Oops, c should be when cos(kx) = 0, work it out from there.
thanks for your time:)
3 answers