1. STANDING WAVES Department of TextileThe Open University of Sri Lanka

2. Content • Objectives • What is a wave? • Principle of superposition • Introduction to standing waves • Conditions that apply for a standing wave • Difference between standing and travelling wave • Standing waves in strings • Standing waves in pipes

3. Objectives After completing this session you should be able to explain what a wave is explain the Principle of superposition explain how standing waves are formed draw the standing waves in closed pipes, open pipes and strings

4. What is a wave ? Wave is a method of transmitting energy by means of large number of oscillations. Oscillations may be mechanical or electromagnetic.

5. Waves continue… Have you ever seen a flag on a windy day? The wind creates waves in the flag. Both the waves in a flag and the ocean are waves that you can see.

6. Principle of Superposition. When two waves are in phase with each other they add together. When two waves are 1800 out of phase with each other they will cancel. (a.) Constructive Interference (b.) Destructive Interference

7. Standing waves When two waves of the same frequency moving in opposite directions super impose, produces a standing or stationary wave. To get an idea about how to form a standing wave, let’s think that a vibration is sent along a string. This may cause to form a wave. This wave will reflect at the other end.

8. Introduction cont.… These incidents and reflected waves will superimpose with each other and form a standing wave (Stationary wave).

9. Conditions for a standing wave Both waves should be in the same frequency The wave length of two waves should be the same Amplitude must be equal or nearly equal to each other Should travel in opposite directions

10. Difference between Standing and Traveling waves Standing waves. • Wave will not move • This is a combination of two waves which move in opposite directions • Stores energy • Consists of nodes and antinodes Traveling waves. • The wave will move • This consists of one wave which moves in one direction • Transmits energy • All particles are vibrating (a.) Standing wave (b.) Travelling wave

11. Standing waves in strings When a wave is propagating along a string its linear mass density can be written as follows. Here , m =Mass of the string L=Length of the string =Linear mass density T= Tension of the string Velocity depends on both tension and linear density.

12. Standing waves in strings. The fundamental vibration mode of a stretched string is seen in the figure. The wavelength is twice the length of the string. Hence Also in a string T=Tension of the string L=Length of the string

13. Physics in a guitar string

14. Standing waves in pipes Many of the practical applications of stationary waves are found in musical instruments like the flute, trombone and clarinet.

15. Standing waves in pipes Pipes with two open ends. As you know already standing waves are formed when two progressive waves of the same medium are moving. You can see that at the closed end of a tube there must be a node, because air molecules couldn’t vibrate when they contact the wall . Open end should have a antinode since it’s air particles are free to vibrations. Pipes with one open end.

16. THE END Published by The Open University of Sri Lanka Author : Mr. L.S.A.Perera Web Content Developer : B. Krishni Perera