What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?

700 m.

Explanation:

Wavelength: This can be defined as the distance in meter required by a wave to complete one oscillation. The S.I unit of of wavelength is meter (m).

the expression connecting velocity, frequency and wavelength is given as,

v = λf Equation 1

Where v = velocity of the earthquake, λ = wavelength of the earthquake, f = frequency of the earthquake.

make  λ the subject of the equation

λ = v/f Equation 2

recall,

v = distance/time

v = d/t Equation 2

Where d = distance, t -= time.

Given: d = 84 km = 84000 m, t = 12 s.

Substitute into equation 2

v = 84000/12

v = 7000 m/s.

Also given: f = 10 Hz.

Substitute into equation 2

λ = 7000/10

λ = 700 m.

Hence the wavelength of the earthquake = 700 m.