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.

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

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

To solve these questions, we'll need to use some basic wave equations and formulas.

1) The relationship between frequency (f), wavelength (λ), and wave speed (v) is given by the equation v = f * λ. We are given the frequency (f = 3.1 Hz) and the wave speed (v = 5.6 m/s). We can rearrange the equation to solve for the wavelength:

λ = v / f

Substituting the given values:

λ = 5.6 m/s / 3.1 Hz ≈ 1.806 m

Therefore, the wavelength of the wave is approximately 1.806 meters.

2) The equation of the wave is given in the form ξ cm = A * sin(kx - ωt), where A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time.

To determine the traveling speed of the wave, we need to find the ratio of the angular frequency (ω) and the wave number (k). The traveling speed (v) is given by v = ω / k.

In the given equation ξ cm = 3.4 sin (1.13x - 0.75t), we can identify that the wave number k = 1.13 (1/cm) and the angular frequency ω = 0.75 (1/s).

Now, let's substitute these values into the equation:

v = ω / k = (0.75 (1/s)) / (1.13 (1/cm))

Since cm and 1/cm cancel each other out:

v = 0.75 (1/s) * (1 cm/1.13) * (100 cm/1 m) = 0.75 * 100 / 1.13 ≈ 66.37 m/s

Therefore, the traveling speed of the wave is approximately 66.37 meters per second.