Police radar detects the speed of a car (Fig. P39.23) as follows. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two microwave signals. The beat frequency is measured. (a) For an electromagnetic wave reflected back to its source from a mirror approaching at speed v, show that the reflected wave has frequency f r 5 c 1 v c 2 v f where f is the source frequency. (b) Noting that v is much less than c, show that the beat frequency can be written as fbeat 5 2v/l. (c) What beat frequency is measured for a car speed of 30.0 m/s if the microwaves have frequency 10.0 GHz? (d) If the beat frequency measurement in part (c) is accurate to 65.0 Hz, how accurate is the speed measurement?

Physics 213 // Week 2 Notes PSU Spring Term, 2017 Chapter 16 Notes (Waves) _____ = Formula Q: What is the difference between mechanical and traverse mechanical waves A: Mechanical waves can exist online in material media. Traverse mechanical waves, like those on a stretched string, are waves in which the particles of the medium oscillate perpendicular to the wave’s direction of travel. Q: What are longitudinal waves A: Waves in which the particles of the medium oscillate parallel to the wave’s direction of travel. Q: What is a sinusoidal wave A: A wave moving in the position direction of an x axis has the mathematical formula: , = ∗ sin − ) Displacement