Two loudspeakers face each other from opposite walls of a room. Both are playing exactly the same frequency, thus setting up a standing wave with distance λ/2 between antinodes. Assume that λ is much less than the room width, so there are many antinodes.

a. Yvette starts at one speaker and runs toward the other at speed v_Y. As the does so, she hears a loud-soft-loud modulation of the sound intensity. From your perspective, as you sit at rest in the room, Yvette is running through the nodes and antinodes of the standing wave. Find an expression for the number of sound maxima she hears per second.

b. From Yvette’s perspective, the two sound waves are Doppler shifted. They’re not the same frequency, so they don’t create a standing wave. Instead, she hears a loud-soft-loud modulation of the sound intensity because of beats. Find an expression for the beat frequency that Yvette hears.

c. Are your answers to parts a and b the same or different? Should they be the same or different?