1. Understand the Concept:

* Echo: An echo is a reflected sound wave.

* Time of Flight: The time it takes for the sound wave to travel to the cliff and back is the total time of flight.

* Speed of Sound: The speed of sound in air is approximately 340 meters per second.

* Period: The period of a wave is the time it takes for one complete cycle.

2. Calculate the Distance Traveled:

* The sound wave travels to the cliff and back, so the total distance traveled is 680 meters * 2 = 1360 meters.

3. Calculate the Time to Travel to the Cliff:

* The echo is heard 4 seconds after the sound is produced, so the time to travel to the cliff is 4 seconds / 2 = 2 seconds.

4. Calculate the Speed of Sound:

* We know the speed of sound is approximately 340 m/s.

5. Understand the Relationship Between Period and Frequency:

* Period (T) and frequency (f) are inversely proportional: T = 1/f

6. Calculate the Frequency:

* We know the speed of sound (v), the distance traveled (d), and the time (t). We can use the formula: v = d/t.

* Rearranging to solve for frequency: f = v/d = 340 m/s / 1360 m = 0.25 Hz

7. Calculate the Period:

* Period (T) = 1 / frequency (f) = 1 / 0.25 Hz = 4 seconds.

Therefore, the period of the wave is 4 seconds.