1BQ1-solns - 1B Midterm 1 Spring 2010 Solutions Problem 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1B Midterm 1 Spring 2010 Solutions Problem 1 Consider a pipe open at one end and closed at the other as shown below. The end (at x=0) begins to vibrate and a travelling sound wave is launched which may be described by: = Re Ae i t kx + ( ) ( ) Here is the horizontal displacement of the air. The wave is reflected from the end (x=L) and a standing wave is set up. Assume there is a node at the speaker and the wave is perfectly reflected at the open end. a) Find the expression for the displacement of the air inside the tube once the standing wave is set up, x , t ( ) . b) Sketch the magnitude of the first three harmonics (lowest and higher two) in the tube showing the nodes and maxima. c) What is the air pressure as a function of x,t in the tube? Solution: Once the wave is reflected. The reflected wave travels in the x direction and there is a phase change of (180 degrees at the solid wall. Therefore: Forward : f = Ae i t kx ( ) reflected : r = Ae i t + kx + ( ) The total wave is the sum of the two: = Ae i t kx ( ) + Ae i t + kx + ( ) = Ae i t e ikx + + e...
View Full Document

Page1 / 7

1BQ1-solns - 1B Midterm 1 Spring 2010 Solutions Problem 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online