The equation, y = 5 sin (3t – 4x), where y is in millimeters, x is in metres and t is in seconds represents a wave motion. Determine the wave’s velocity of propagation.*1 point0.50 m/s0.75 m/s1.0 m/s1.2 m/s
Question
The equation, y = 5 sin (3t – 4x), where y is in millimeters, x is in metres and t is in seconds represents a wave motion. Determine the wave’s velocity of propagation.*1 point0.50 m/s0.75 m/s1.0 m/s1.2 m/s
Solution 1
The velocity of a wave is given by the formula v = ω/k, where ω is the angular frequency and k is the wave number.
From the given wave equation, y = 5 sin (3t – 4x), we can identify the values of ω and k.
The coefficient of t (time) is the angular frequency ω. So, ω = 3 rad/s.
The coefficient of x (distance) is the wave number k. So, k = 4 rad/m.
Now, we can substitute these values into the formula for velocity:
v = ω/k = 3 rad/s / 4 rad/m = 0.75 m/s.
So, the wave's velocity of propagation is 0.75 m/s.
Solution 2
The velocity of a wave is given by the formula v = ω/k, where ω is the angular frequency and k is the wave number.
From the given wave equation, y = 5 sin (3t – 4x), we can identify that ω = 3 (from the coefficient of t) and k = 4 (from the coefficient of x).
Substituting these values into the formula, we get:
v = ω/k = 3/4 = 0.75 m/s
So, the velocity of propagation of the wave is 0.75 m/s.
Similar Questions
A wave is represented by :y (x, t) = (5 cm) sin 1(20 s ) t− 1(15 cm ) x− + Determine the velocity of the wave.
b) Determine the speed and acceleration at t = 0.500 s for the particle on the wave located at x = 5.0 cm.
A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m−1 x). What is the velocity of the wave?
A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation x(x, t) = 2.10 cm cos(2000 rad/s t + 40.0 m−1 x). What is the velocity of the wave?
A sinusoidal wave traveling in the +𝑥 direction (to the right) has an amplitude of 15.0 cm, a wavelength of 10.0 cm and a frequency of 20.0 Hz. At t = 0, a particle at x = 0 has a displacement of 15.0 cm.(a) Write an expression for the wave function, y(x, t).20:39b) Determine the speed and acceleration at t = 0.500 s for the particle on the wave located at x = 5.0 cm.20:40
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.