It takes a wave traveling on a string 1.2 s to complete a full cycle. You measure the distance it takes to repeat itself to be 1.8 m. How fast is the wave moving?

1.5 m/s.

Explanation:

The Speed of a wave is the product of the wavelength and its frequency or it is the ratio of it wavelength and its Period. It can be expressed mathematically as

V = λf or λ/T ... Equation 1

Where V = speed of the wave travelling on the string, λ = wavelength of the wave, T = period of the wave, F = frequency of the wave.

Given: λ = 1.8 m (distance it takes to repeat itself), T = 1.2 s (Time taken to complete a full cycle)

Substitute into equation 1

V = 1.8/1.2

V = 1.5 m/s.

Hence the wave is 1.5 m/s fast.