Question

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?

Answer 1

Answer:

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.

Answer 2

Answer:

700m (or 0.7km)

Explanation:

The wavelength (λ) of a particle (in this case, earthquake) is related to the frequency (f) of oscillation of the particle and the speed (v) of the particle as follows;

v = fλ

=> λ = $\frac{v}{f}$  -----------------------(i)

But;

v = $\frac{s}{t}$       -------------------(ii)

Where

s = distance

t = time taken

From the question;

s = 84.0km = 84000m

t = 12.0s

Substitute these values into equation (ii) to get the speed of the earthquake as follows;

v = $\frac{84000}{12.0}$ m/s

v = 7000m/s

The speed of the earthquake is 7000m/s.

Now using the values of the speed (v = 7000m/s) and the given frequency of 10.0Hz, calculate the wavelength of the earthquake by substituting them into equation (i) as follows;

λ = $\frac{7000}{10.0}$

λ = 700m

Therefore, the wavelength of the earthquake is 700m