Propagation of a transverse wave

Question

A transverse wave propagates in the positive x-direction with a wavelength of a 0.3 m and a period of 10^-3 s.

a) use y=Acos(2π(x/λ ± t/T)) to write down an expression for this wave.

b) What are the frequency and angular frequency of the wave?

c) What is the propagation velocity of this wave?

Answer 1

a) Since the wave is propagating in the positive x-direction. Then the wave is governed by

y = Acos(2π(x/λ - t/T))

but the wavelength, λ = 0.3m and period, T = 10^-3s

==> y = Acos(2π(x/0.3 - t/10^-3)) = Acos(2π(3.3x - 1000t))

b) frequency, f = 1/T = 1/10^-3 Hz = 1000 Hz and angular frequency, ω = 2πf = 2000π rad/s

c) the velocity, v is defined by v = λf = .3m(1000s^-1) = 300m/s