The displacement of a wave traveling in the positive x-direction is y (x, t) | = (3.5 cm) cos (2.7x - 92t), where x is in m and t is in s. What are the (a) frequency, (b) wavelength, and (c) speed of this wave?

Answer

Given,

y (x, t) = (3.5 cm) cos (2.7 x - 92 t)

comparing the given equation with general equation

y (x, t) = A cos (k x - ω t)

A = 3.5 cm, k = 2.7 rad/m, ω = 92 rad/s

we know,

a) ω = 2πf

f = 92 / 2π

f = 14.64 Hz

b) Wavelength of the wave

we now, k = 2π/λ

2π/λ = 2.7

λ = 2 π/2.7

λ = 2.33 m

c) Speed of wave

v = ν λ

v = 14.64 x 2.33

v = 34.11 m/s