Physics 7C Fall 2008Lecture 4 Standing Waves Hitting an Interface Ray Representation Beginning Optics
Standing Waves • Applet from Santa Barbara City College shows two interfering waves: http://www.cs.sbcc.edu/~physics/flash/oscillationswaves/standingwaves.html
Reaching the end of a medium “Incident” Observe reflection on the wave machine…
Hitting an Interface • Upright • Inverted
Hitting an Interface • Reflection and Transmission “Incident” “Reflected” “Transmitted” “Transmitted” or “Reflected”
Wavefronts and Rays • A wavefront represent points of equal phase (e.g. the crest of the wave). • The ray shows the direction in which the wavefront is moving. • Rays are perpendicular to wavefronts.
From spherical to planar wavefronts • Spherical wave front • Planar wave front
Identify the representation: 1 2 Both wavefront Both ray 1 is wavefront, 2 is ray 1 is ray, 2 is wavefront
What (typically) happens next? 1 2 There is a reflected wave There is a transmitted wave Both reflected and transmitted waves Neither reflected nor transmitted waves
Reflected Ray • Throw a ball at a wall, view from above. Which is the correct path, assuming a perfectly elastic collision? (a) (b) (c) (d) Depends
Reflected Ray Law of Reflection: i=r Normal Line Angle of Incidence Angle of Reflection
Reflected Wavefronts Law of Reflection: i=r Normal Line Angle of Incidence Angle of Reflection
Transmitted Ray: • Drive a car from a well-paved road into rough grass. Which way will it go? (a) (b) (c)
Transmitted Ray: • Transmitted ray is bent, or “refracted” Angle of Incidence Law of Refraction or “Snell’s Law:” n1sin1=n2sin2 n : “index or refraction” speed of light in vacuum speed of light in material Angle of Refraction
Observe the Water Compass • In which medium does light travel faster? • Air • Water • Same in both
Standing Waves & Beats • It is 1709 and your very good friend Johann Sebastian Bach has just arrived in Weimar and wants to remodel the organ of the Weimar court chapel. He writes you in a letter to ask for your help in figuring out the length of one of the organ pipes. He has the following information for you. He has one pipe that is open at both ends and one pipe that is open at one end only. He tells you that when he excites the second-lowest frequency of the pipes, the resulting beat frequency is exactly the same as the beat frequency caused by exciting the third- lowest frequency of each pipe. Given that the length of the pipe that is closed at one end is 1.0 m, he asks you to find the length of the pipe that is open at both ends. This quiz has more steps that could potentially bog you down than the one you will take on Tuesday. You should be able to demonstrate that L=1.25m works!