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26 Common Questions of a Traveling Wave Equation

physics.fisikastudycenter.com-Learning traveling wave, in 15 common questions of a traveling wave equation. You might drive the additional questions up to 26 if you want.

Problem.
Given an equation of a traveling wave Y = 0,02 sin (10πt − 2πx)
t, y and x are in second, meter and meter.

Questions
Find the 15 items of the equation above:
1. amplitude
2. angular frequency
3. wave number
4. speed
5. frequency
6. period
7. wavelength
8. traveling direction
9. displacement when t = 1 second and x = 1 m
10. equation of speed
11. maximum speed
12. equation of acceleration
13. maximum acceleration
14. phase angle when t = 0,1 at x = 1/3 m
15. phase when t = 0,1 second at x = 1/3 m

Answer :
The equation of a traveling wave given by:
Y = A sin (ωt - kx)
where A is the amplitude of wave, ω is the angular frequency with ω = 2πf and k is wave constant where k= 2π/λ so then we get the answers :
1. A = 0,02 m
2. ω = 10π rad/s
3. k = 2π
4. v = ω/k = 10π/2π = 5 m/s
5. f = ω/2π = 10π/2π = 5 Hz
6. T = 1/f = 1/ 5 = 0, 2 second
7. λ = 2π/k = 2π/2π = 1 m
8. the direction is along the x positive
9. Y = 0,02sin(10 π- 2π)=0,02sin(8π)= 0 m
10. v = ω A cos(ωt−kx)=10π(0,02) cos(10πt−2πx) m/s
11. vmaks = ωA = 10π(0,02) m/s
12. a = −ω2y=−(10π)2 (0,02)sin(10πt−2πx) m/s2
13. amaks =|−ω2A|=|−10π2 (0,02)| m/s2
14. phase angle θ = (10.π.0,1−2π.(1/3)=1/3 π = 60o
15. phase φ = 60o/360o = 1/6

Try to use your own traveling wave equation and you shouldn't have any difficulties to answer these following questions for instance:
a. the form of traveling wave equation you have i.e: Y = A sin (ωt - kx) or Y = A sin (ωt + kx)
b. the amplitude
c. the angular frequency
d. the frequency
e. the period
f. the wave number
g. the wavelenght
h. the speed
i. the displacement when t = 1 second at x = 1/8 m
j. the phase angle when t = 1 sekon and x = 1/12 m
k. the phase when t = 1 second at x = 1/9 m
l. the form of speed equation
m. the speed equation
n. the speed when t = 1 second at x = 1/8 meter
o. the form of acceleration equation
p. the acceleration equation
q. the acceleration when t = 1 second
r. the forms of maximum values of speed and acceleration
s. the maximum value of speed
t. the maximum value of acceleration
u. the phase difference of two points with 25 cm in separation distance
v. the phase angle difference of two points with 25 cm in separation distance
w. the distance of two points with the phase angle difference of ¼ π radian
x. the distance of two points with phase angle difference of 60°
y. the distance of two points with phase difference of ½
z. the direction of traveling

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