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?
Question
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?
Solution
The velocity of a wave can be determined using the wave equation, which is given by:
v = ω/k
where:
- ω is the angular frequency, and
- k is the wave number.
From the given wave equation, we can identify that:
ω = 2000 rad/s (angular frequency) k = 40.0 m^-1 (wave number)
Substituting these values into the wave equation gives:
v = ω/k v = 2000 rad/s / 40.0 m^-1 v = 50 m/s
So, the velocity of the wave is 50 m/s.
Similar Questions
A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation z(z, t) = 1.2 cm cos(1800 rad/s t + 60 m−1 z). What are the wavenumber and direction of propagation of the wave?
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 wave is represented by :y (x, t) = (5 cm) sin 1(20 s ) t− 1(15 cm ) x− + Determine the velocity of the wave.
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
Longitudinal wave is produced on a slinky. The frequency of the wave pulse is 60Hz and it travels with a speed of 30 cm/s. The separation between two consecutive compressions is-
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.