This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: EXPERIMENT STANDING WAVES ON A STRING Introduction: A wave is the propagation of a disturbance or energy. A wave is characterized by its wavelength λ , the frequency of oscillation f (in Hz or 1 /s = s − 1 ), and the wave speed v . These quantities are related by the fundamental equation of wave motion: λ f = v (1) When a stretched cord or string is disturbed, a wave travels along the string with a speed that depends on the tension F in the string and its linear mass density μ (mass per unit length): μ F v = (2) In SI units, v is in m/s , F is in Newtons and μ is in kg/m . Waves in a stretched string are transverse waves. Upon reaching a fixed end of the string, the wave is reflected back along the string. For a continuous disturbance, the propagating waves interfere with the oppositely moving reflected waves and a standing or stationary wave pattern is formed under certain conditions (see Figure 1). Some points on the string are stationary i.e. there is no displacement of the string at these points at any time. These positions are called nodal points or nodes , and the points of maximum displacement are called antinodes . Nodes and antinodes exist only in standing waves. Node Antinode n = 1 λ n = 2 n = 3 L λ /2 Figure 1 Standing Waves. The length of one loop is equal to λ /2 A cord may be forced to vibrate with any frequency but will vibrate with maximum amplitude if the frequency f , the length of the cord L , and the speed of the wave on the cord v are so related that standing waves are set up. With both ends of the cord fixed in position the ends must be nodes in the standing waves are set up....
View Full Document
This note was uploaded on 04/01/2011 for the course PHY 135 taught by Professor Wagihghobriel during the Spring '11 term at University of Toronto.
- Spring '11