find the frequency, period and speed of wave

Question

the equation, y=5sin(3x-4t),

 

where y is in millimeter and t is in seconds represents a wave motion.

 

determine the frequency, period and speed of the wave

Answer 1

You are given an equation of the form 

 

y = A sin(kx - ωt)

 

ω = angular frequency = 4 rad/s

 

f = linear frequency = ω/(2π) = 4/(2π) Hz = 0.6366 Hz

 

T = period = 1/f = 1/0.6366 s = 1.571 s

 

v = speed = λ/T

 

You need to state the units of x.  You need to know the units of x in order to correctly assign units to k.  That was not included included in the problem statement.  I will assume x is in millimeters.  

 

k = 2π/λ

 

k = 3 mm^-1 

 

λ = 2π/k = 2π/(3 mm^-1) = 2.094 mm

 

v = speed = λ/T = (2.094 mm) / (1.571 s) = 1.333 mm/s