Question

To understand the standard formula for a sinusoidal traveling wave.
One formula for a wave with a y displacement (e.g., of a string) traveling in the x direction is
y(x,t)=Asin(kxâÏt).
All the questions in this problem refer to this formula and to the wave it describes.
1) What is the phase Ï(x,t) of the wave?
Express the phase in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï
Ï(x,t)=
2) What is the wavelength Î» of the wave?
Express the wavelength in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
Î»=
3) What is the period T of this wave?
Express the period in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
T=
4) What is the speed of propagation v of this wave?
Express the speed of propagation in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
v=

1. phucdien

1) Φ=zero

2)  λ = 2π / k

3)   T = 2π / w

4)  v = w / k

Explanation:

The equation of a traveling wave is

y = A sin (ka – wt + Ф)

Let’s answer using this equation the different questions

1) we see that the equation given in the problem the phase is zero

2) wavelength

k = 2π /λ

λ = 2π / k

3) The perido

angular velocity is related to frequency

w = 2π f

frequency and period are related

f = 1 / T

w = 2 π / T

T = 2π / w

4) the wave speed is

v = λ f

λ = 2π / k

f = w / 2π

v = 2π /k  w /2π

v = w / k