Atraveling wave has displacement given by y(x, t)=(2.0cm)×cos(2πx−4πt), where x is measured in cm and t in s. what is the speed of the wave?

v = 2 cm/s

Explanation:

The equation of the wave is

y(x,t)   =  (2.0cm)*cos(2π*x−4π*t)

Where,

x is measured in cm

t in s

A more general formula for this equation would be

y(x,t)   =  A*cos(k*x−ω*t)

Where,

A = amplitude.

k = the wavenumber

ω = the angular frequency

The velocity of the wave corresponds to

v = ω/k

v = 4π / 2π = 2 cm/s

v = 2 cm/s

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west