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**.

- How far is Ollie from Joe?
- How fast is Ollie moving, and in which direction?
- What is the frequency
**f3**of these echoes according to Joe?

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.

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?"

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