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.
700m (or 0.7km)
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 = [tex]\frac{v}{f}[/tex] -----------------------(i)
But;
v = [tex]\frac{s}{t}[/tex] -------------------(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 = [tex]\frac{84000}{12.0}[/tex] 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 = [tex]\frac{7000}{10.0}[/tex]
λ = 700m
Therefore, the wavelength of the earthquake is 700m
