Question

1) A wave with frequency 3.1 Hz and amplitude 2.7 cm moves in the positive x-direction with speed 5.6 m/s. Determine the wavelength.

2) The equation of a wave along the x-axis is given as: ξ cm = 3.4 sin (1.13 x - 0.75 t)
in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
Determine the the traveling speed of the wave.

Answer 1

1) A wave with frequency 3.1 Hz and amplitude 2.7 cm moves in the positive x-direction with speed 5.6 m/s. Determine the wavelength.

Distance = rate * time
here the time is a period 1/f = 1/3.1
distance = 5.6 m/s * (1/3.1) s

Answer 2

2) The equation of a wave along the x-axis is given as: ξ cm = 3.4 sin (1.13 x - 0.75 t)
in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
Determine the the traveling speed of the wave.

if x changes by L with no change in t, the argument of the sin increases by 2 pi
(1.13 x - 0.75 t) +2pi = 1.13 (x+L) -.75 t
so
2 pi = 1.13 L
L = 2 pi/1.13

if t changes by T with no change in x, the argument of the sine changes by 2pi
1.13x -.75 (t) = 1.13x -.75(t+T)+ 2 pi
2 pi = .75 T
T = 2 pi/.75
rate = distance/time = (2 pi/1.13) /(2 pi/.75) = .75/1.13

By the way, you can do this by looking for the constant phase speed
express the argument of the sine as
(2 pi/L)(x-vt)
then 2 pi/L x = 1.13 x
and (2 pi/L)(vt) = .75t
or
L = 2 pi/1.13
v = .75L/2 pi = .75/1.13 again