Final answer:
The wavelength of an earthquake with a frequency of 10.0 Hz that reaches another city 84.0 km away in 12.0 s is 700 m. This is calculated using the formula for wave speed (velocity = frequency × wavelength) after determining the wave velocity.
Step-by-step explanation:
The calculation of the wavelength of an earthquake requires the understanding of basic wave properties such as frequency and velocity. The velocity of a wave (v) can be calculated by multiplying its frequency (f) by its wavelength (λ): v = f × λ. In the given problem, we can calculate the seismic wave velocity by dividing the distance (84.0 km) by the time (12.0 s), which gives us a velocity of 7000 m/s. Knowing the frequency of the earthquake is 10.0 Hz, we can then use the formula to find the wavelength: λ = v / f. Thus, the wavelength of the earthquake wave would be 700 m.
To apply this to real-world scenarios, engineers and seismologists study the effects of earthquake wavelengths on structures to help design buildings that can withstand seismic activity. As earthquakes propagate through the Earth, the interaction of waves with structures of different heights can lead to resonance, amplifying the effects of the earthquake in some buildings while sparing others.