2. CONTENTS Formation, structure and terminology In pipes Wavelength and L (length), velocity o Experiments are not described in this power point. o Observing stationary waves - p.198 o Microwaves - p.199 o Determining the speed of sound – class notes Harmonics and overtones Similarities and differences

3. FORMATION, STRUCTURE AND TERMINOLOGY A stationary wave is formed whenever two progressive waves of the same amplitude and wavelength, travelling in opposite directions, superimpose (p. 197) These two waves may originate from different sources, but most often is created by a single wave being reflected so that the reflected wave interferes with the initial wave. Stationary waves can be created with either transverse or longitudinal waves.

4. Formation due to reflection The animation below shows a wave train moving toward the right, incident upon a boundary. As the incident wave train is reflected from the free end, a standing wave is quickly formed as the incident wave is superposed with the left- going, reflected wave. The standing wave neither moves right or left, but simply oscillates up and down. Points on the string that do not move (where the amplitude is zero) are called nodes. Locations where the standing wave pattern has a maximum amplitude are called anti-nodes.

5. The black signal in the animation represents the superposition of these two oppositely directed traveling waves. Both waves have the same amplitude, the same frequency, and the same wavelength. The amplitude of this standing wave is twice that of the individual waves when the two waves are in phase so that peaks and valleys line up. The amplitude of the standing wave is zero when the two waves are completely opposite phase so that they peaks of one wave line up with the valleys of the other wave; the two wave amplitudes cancel each other out.

6. Structure (both ends fixed, strings or pipes) N: Node – particle always at zero displacement, ie does not move. The distance between two adjacent nodes = ½ A: Anti-node – particle at this point capable of oscillating with maximum amplitude. Particles in other positions are not able to move this far, and have smaller amplitudes. Representation Actual Movement N A N

7. Standing Sound Wave All of the animations have been taken from the website below. Please visit the site for more detailed information http://www.acs.ps u.edu/drussell/De mos/StandingWa ves/StandingWav es.html http://www.acs.ps u.edu/drussell/De mos/StandingWa ves/StandingWav es.html

8. Structure (fixed ends)

9. Structure (pipes, one end closed_

11. Structure (tubes open on both ends) There is always an anti-node, A, at an open end. The air moves freely here, with maximum amplitude, in a direction parallel to the sides of the pipe. The distance from an anti-node to the adjacent node is always ¼. A N A

12. Wavelength, L (length) and velocity The velocity of sound is a constant, so would be about 340ms -1 regardless of what mode of vibration is being described; or whether the pipe is open or closed. Always remember, the distance between adjacent nodes = ½ The distance between a node and an antinode is ¼ Put the correct number of 1/2 = L (the length of the string or pipe) to find l (or count how many 1/4 are in the open ended pipe) Make the subject Use the wave equation if necessary (v = f )

13. Quiz 1. Draw the fundamental pattern for a stationary wave on a string with both ends fixed. 2. The length of the string is 50cm. Calculate the wavelength of this wave in metres. ANSWER - 1m

14. Quiz (last 2 questions) 3. Draw the third harmonic pattern for a stationary wave on a string with both ends fixed. 4. The length of the string is 50cm. Calculate the wavelength of this wave in metres. ANSWER – 0.33m

15. Harmonics and Overtones (strings)

19. Similarities between standing and progressive waves 1. Energy is seen as vibrations or oscillations of particles. These vibrations are at right angles to the direction of propogation for transverse waves, and are in the same direction as propogation for a longitudinal wave.

20. Differences between standing and progressive waves 1. There is no net transfer of energy with a standing wave 2. A standing wave has nodes (points where particles always have zero displacement) 3. A standing wave has antinodes (points where oscillating particles have maximum amplitude) 4. A standing wave has particles which have different amplitudes depending on their position. The closer the particle is to a node, the smaller its amplitude will be. With a progressive wave, all points will reach maximum displacement at some point in time. They all have the same possible amplitude, even though they may reach that point at different times.