Standing Waves Elliott Basics Sometimes waves appear to

Standing Waves Elliott

Basics • Sometimes waves appear to be standing still We can see them in water, especially water surrounded by walls. We call them standing waves or stationary waves. • Any kind of wave can form a standing wave.

Real Life Applications Musical instruments depend on standing waves: • In a string, for example guitar, pianoforte, violoncello. • In a column of air, e. g. clarinet, tuba, organ.

Recap Standing waves are formed when two progressive waves are superposed of: • Equal frequency • Nearly the same amplitude • Same speed • Travelling in opposite directions.

Reflection and Phase Change If we send an incident wave down a string, which is fixed at the end, the wave is reflected at the fixed end and undergoes a phase change of π radians or 180 o. There is no phase change at the free end.

Check Your Progress What are the conditions needed for a standing wave?

Answer Equal frequency; Nearly the same amplitude; Same speed; Travelling in opposite directions.

Constructive Interference The phase change of π radians causes cancellation at the fixed end. This region of zero displacement is called a node.

Nodes and Antinodes

Check Your Progress What is meant by a node and an antinode? A standing wave loop in a string is 66 cm long. What is the wavelength in metres?

Answer Node – a point of zero displacement in a standing wave; Antinode - the point of maximum displacement; Loop is ½ wavelength therefore the wavelength is 0. 66 × 2 = 1. 22 m

Comparing Waves – Stationary waves • The amplitude varies according to position from zero at a node, to maximum at an antinode. The amplitude of a given point is always the same. • The phase difference between two particles is zero if the points are between adjacent noted. It is 180 o if they are either side of a node.

If the points are a separated by an even number of nodes, they are in phase. Therefore P and Q are in phase with each other (as are R and S, and T and U). P and S are in antiphase, but P is in phase with U.

Standing Waves on a String - Rules • • • At the fixed end in a string, there is always a node. A string in a musical instrument is always fixed at both ends. Therefore there is a node at each end. There is an antinode halfway down. At twice the fundamental frequency, there is a node in the middle of the string.