1. Waves

2. Nature of Waves  Harmonic motion involved cyclic changes in position over time.  Wave motion involves changes in position in time and space.

3. Wave Properties  Waves have an amplitude. Maximum displacement from equilibrium  Waves have a speed. Change in wave position with time.  Waves can be a single pulse or a continuous stream of pulses. Continuous waves have a period A xx v =  x /  t

4. Energy Transport  The points on the material don’t move with the wave.  The wave shape moves, and so does the energy.

5. Transverse Waves  A wave the undulates at right angles to the direction of propagation is a transverse wave. Measure  y(x,t)Measure  y(x,t) 1 wavelength yy x Time must be shown as a sequence of graphs

6. Longitudinal Waves  A wave the undulates in the same direction of propagation is a longitudinal wave. Measure  x(x,t)Measure  x(x,t) 1 wavelength xx x Time must be shown as a sequence of graphs

7. Water Waves  Some wave are combinations of longitudinal and transverse waves. A point of water will travel in a circle (or ellipse)A point of water will travel in a circle (or ellipse) The separation of peaks is the wavelength The frequency of peaks in space is the wavenumber k, k = 2 

8. Wave Speed  For a continuous wave the speed is the wavelength compared to the period.  On a string with some mass the speed is related to the tension. 1 wavelength = linear mass density = 

9. Rock Climbing  Two climbers are joined by a 43-m rope of 5.0 kg. One climber strikes the rope and 1.4 s later the other climber feels it.  What is the rope tension?  The expression for tension is  The mass density and speed  With values F T = 110 N next