PHYS-302, Physics of Waves (Summer 2007)

W5 - Reflection of Waves from Boundaries (Chapter 5)

Topical Outline for two-hour class:

• Transverse Waves on a String - we started class by deriving the wave equation for transverse displacement waves on a string.
• Reflection from a Hard Boundary - we then looked at what happened to a wave function on a string when it reflects from a rigid (fixed) boundary. The displacement must be zero a the fixed boundary. This means that the wave reflecting from the fixed end is inverted, with opposite polarity compared to the incident wave.
• Reflection from a Soft Boundary - the free end of a string has no force, and therefore the string has zero slope at the free end. When the wave reflects from a free end it reflects upright, with the same polarity as the incident wave.
• Standing Waves on a Fixed-Fixed String - Knowing that waves reflecting from a fixed end are inverted, we investigated sinusoidal waves traveling on a string fixed at both ends, and found that
• Hands-on Activity (Reflection of Pulses) -
• Reflection of Waves from an Impedance Discontinuity -

Hands-on Activities

Reflection of Sound Waves in a Pipe A single cycle pulse of a 5000 Hz sine wave was fed to a small loudspeaker at one end of a 80cm length of 1" diameter PVC pipe. A small electret microphone was inserted into the pipe right in front of the speaker. The pressure variation due to the sound wave pulse was measured as the wave pulse passed the speaker on the way down the pipe and after it reflected from the other end, which was either closed with a rigid cap, open to the room, or filled with cotton balls. The data below shows that when a pressure wave reflects from a rigid boundary (closed end), the reflected wave is has the same polarity (orientation) as the incident wave. A wave pulse reflects from a soft boundary (open end) with the opposite, or negative, polarity as the incident wave. When the end of the pipe is stuffed with cotton, the incident wave is almost completely abosrbed, and very little wave amplitude reflects back down the pipe.
Reflection of E&M waves in a coaxial cable A single cycle of a 10-MHz sine wave was sent down a 180m length of 50-ohm coaxial cable on a spool (such a long length is needed because of the fast speed of E&M waves). A very fast oscilloscope with microsecond resolution was used to observe the inicident signal as well as the reflection from the other end. The other end of the coaxial cable was either an open circuit, a short circuit, or bridged with a 51-ohm termination. The data below shows that the pulse reflects from the open circuit end with the same polarity as the incident wave, but that it is inverted from the short circuit termination. The 51-ohm resistor nearly exactly matches the impedance of the cable, and there is no reflected wave.
Electromagnetic pulse in a coaxial cable reflects from an open circuit end with the same polarity (upright). Electromagnetic pulse in a coaxial cable reflects from a short circuit with the opposite polarity (upside down) Terminating the end of the coaxial cable with a 50-ohm resistor provides an impedance match, and the incident E&M is almost entirely absorbed (dissipated in the resistor). Back to "Physics of Waves"