When you walk with a cup of coffee (diameter 8 cm) at just the right pace of about one step per second, the coffee sloshes higher and higher in your cup until eventually it starts to spill over the top.

A. Estimate the speed of the waves in the coffee.

B. What is the formula to find the speed of the waves?

A. The speed of the waves in the coffee is 16 cm per second

B. Velocity = frequency X wavelength

Explanation:

A.

We can consider the coffee in the cup to be in a standing wave mode. This means that the position of the peak amplitude profile does not move in space. This means that the nodes of the wave are at the ends of the cup which is 8 cm in length.

Consequently, the diameter of the whole cup is equal to half the wave length.

The full wave length is now equals to 2 X diameter of cup = 16 cm.

The frequency of the wave can be seen to be to be at one step per second.

Hence, using the wave formula, Velocity of wave = frequency X wavelength,

we have that velocity of wave = 1 X 16 = 16 cm / second

B

Formula for speed of waves is

Velocity of waves = frequency of oscillation X wave length