Courtesy of the Swiss Cetacean Society

Joe Orca lives in the sea, where sound waves travel at roughly 1500 m/s.

On Monday, he floats motionless after waking up. He sends out a short pulse of sound waves North at a frequency f1 = 10,000 Hz. Exactly 3.0 seconds later, his pal Ollie Orca is struck by the pulse. Ollie perceives the pulse to have a frequency f2 = 9,900 Hz.

1. How far is Ollie from Joe?
2. How fast is Ollie moving, and in which direction?

Some of the sound waves bounce off Ollie. The frequency of these reflected waves, according to Ollie, is the same frequency f2 = 9,900 Hz that Ollie perceives. The waves travel back to Joe, who is still floating motionless.

3. What is the frequency f3 of these echoes according to Joe?

Tuesday, as he swims North lazily at v = 3 m/s, he sends out a short pulse of sound waves at a frequency f1 = 10,000 Hz. Exactly 5.2 seconds later, he hears an echo ... but the frequency is now f3 = 10,145 Hz.

"Hmmm," thinks Joe, "could this be lunch?"

1. How far is the target from Joe?
2. How fast is the target moving, and in which direction?
3. If both parties continue at their current velocities, how long until they meet?

P.S. Orcas can be just plain nasty.