Transverse Speed of a particle on a wave

Click For Summary
SUMMARY

The maximum transverse speed of a particle on a wave described by the equation y = 6.0sin(0.012πx + 4.9πt) is determined by taking the time derivative of the transverse displacement. The initial calculation of the speed at t = 0 yields y' = 6 * 0.012πcos(0.012πx), but this only represents the spatial derivative. The correct approach requires calculating the time derivative, leading to the conclusion that the maximum transverse speed is derived from the full time-dependent wave equation.

PREREQUISITES
  • Understanding of wave equations and their properties
  • Knowledge of calculus, specifically derivatives
  • Familiarity with trigonometric functions and their derivatives
  • Basic physics concepts related to wave motion
NEXT STEPS
  • Study the concept of wave speed and its relation to frequency and wavelength
  • Learn how to compute derivatives of trigonometric functions in the context of wave equations
  • Explore the relationship between transverse speed and wave parameters
  • Investigate the effects of different waveforms on particle motion
USEFUL FOR

Students in physics or engineering, particularly those studying wave mechanics, as well as educators looking for examples of wave motion and calculus applications.

Oijl
Messages
102
Reaction score
0

Homework Statement


The equation of a transverse wave traveling along a very long string is given by y = 6.0sin(0.012pi*x + 4.9pi*t), where x and y are expressed in centimeters and t is in seconds.

Find the maximum transverse speed of a particle in the string.


Homework Equations





The Attempt at a Solution


I want the speed, or rate of change of position, or derivative of position. The given equation represents the transverse displacement, so, at t = 0, I would have y' = 6*0.012picos(0.012pi*x). Since y(x, t) is a sine function, the greatest slope would be at (0, 0), so y'(0, 0) would represent the greatest rate of change of y(x, t).

So the maximum transverse speed of a particle in the string would be 6*0.012*pi, correct?

This, however, is not the right answer, so why not?
 
Physics news on Phys.org
You have to take the derivative with respect to time.
 
The speed is the time derivative.
 

Similar threads

Find transverse velocity given an equation of displacement
  • · Replies 9 ·
Replies
9
Views
3K
Distance traveled by a particle in a transverse wave
  • · Replies 2 ·
Replies
2
Views
3K
Waves and vibrations on a string
  • · Replies 2 ·
Replies
2
Views
2K
Standing wave transverse motion and amplitude
  • · Replies 5 ·
Replies
5
Views
2K
Wave function - displacement - transverse wave
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of power in a traveling wave on a string
  • · Replies 9 ·
Replies
9
Views
2K
Waves on a String -- Minimizing reflections from the far end (ring on a bar)
  • · Replies 1 ·
Replies
1
Views
2K
How Do You Calculate Max and Min Transverse Speeds in a Wave on a String?
  • · Replies 1 ·
Replies
1
Views
4K
Propagation of transverse pulse on a string
  • · Replies 6 ·
Replies
6
Views
2K
Question about Waves on a String
  • · Replies 2 ·
Replies
2
Views
2K