Physics

Problem

Seismic waves produced by an earthquake consist mainly of two types: longitudinal (P) waves and transverse (S) waves. At the epicentre the two waves start at the same instant. (i) A P‐wave recorded by instruments has a wavelength of

2.5\,\text{km}

and a frequency of

5\,\text{Hz}

. Calculate its speed. (ii) An S‐wave from the same earthquake has a wavelength of

1.5\,\text{km}

and a frequency of

3\,\text{Hz}

. Calculate its speed. (iii) A seismograph station is situated

200\,\text{km}

from the epicentre. Using your answers to parts (i) and (ii), compute the time interval between the arrival of the P‐wave and the S‐wave at the station. (iv) State which of the two waves is transverse and mention one characteristic feature of particle motion for that wave type.

Intuitive explanation

The key to seismic waves is the fundamental wave equation $v = f\lambda$ : multiply frequency by wavelength to find how fast each wave travels through Earth's crust. Once you know both speeds, you can calculate arrival times at a distant station—the difference tells you which wave arrived first and by how much. This time delay is actually how seismologists locate earthquakes!

Intuitive explanation

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