Question

A seismograph located 1200 km from an earthquake detects seismic waves 5 minutes after the quake occurs. The seismograph oscillates in step with the waves at 2 Hz. Find the wavelength in km.

Answer 1

To solve this problem we will apply the given relationship between wavelength, speed and frequency as well as the use of kinematic equations of motion description.

The wavelength is directly proportional to the speed and inversely proportional to the frequency, in other words,

$\lambda = \frac{v}{f}$

Where

v = Velocity

f = Frequency

Speed is not given but if the distance traveled in a certain time, that is

$v = \frac{d}{t}$

Replacing

$v = \frac{1200km}{5min}$

$v = \frac{240km}{min}(\frac{1min}{60s})(\frac{1000m}{1km})$

$v = 4000m/s$

Substituting this value at our first equation we have

$\lambda = \frac{v}{f}$

$\lambda = \frac{4000}{2}$

$\lambda = 2000m$

Therefore the wavelength of the seismic wave is 2000m