Negative propagation of a transverse wave

Question

A transverse wave propagates in the negative x-direction with a frequency of 20 Hz and a propagation velocity of 25 ms^-1.

a) What are the wavelength, period, and angular frequency of this wave?

b Use y=Acos(2π(x/λ ± t/T)) to write down and expression for this wave

Answer 1

a) the wavelength, λ is defined by λ = v/f [where v is the velocity and f the frequency]

the period, T = 1/f and the angular frequency, ω =2πf

Hence, λ = v/f = (25ms^-1)/20s^-1 = 1.25 m

T = 1/f = 1/20s^-1 = 0.05 s

ω = 2πf = 40π rad/s

b) since the wave propagation is in the negative x-direction, then the wave is governed by the equation

y = Acos(2π(x/λ + t/T)) = Acos(2π(x/1.25 + t/0.05)) = Acos(2π(0.8x + 20t))