Understanding P and S Seismic Body Waves

Secondary Waves (S Waves)

Following the P wave is the S wave, or Secondary wave. S waves are slower than P waves, which is why they arrive at a recording station with a noticeable time delay.

S waves are shear waves (or transverse waves). Unlike the push-pull motion of P waves, S waves move the medium perpendicular to the direction of the wave's travel. If you were to shake a rope up and down, the wave travels toward the end of the rope, but the rope itself moves up and down. This "side-to-side" or "up-and-down" motion is characteristic of shear waves.

The most defining characteristic of S waves is their limitation: they can only travel through solids. Liquids and gases do not possess "shear strength"—they cannot resist a change in shape when pushed from the side; they simply flow. Because S waves require a medium that can spring back to its original shape after being sheared, they are completely stopped by liquid layers.

Exam Tip: If a question asks how we know the Earth's outer core is liquid, look for the "S-wave shadow zone." The fact that S waves cannot pass through the center of the Earth proves that a liquid layer must be blocking them.

Summary of Differences

To help differentiate these waves for study purposes, we can compare them across three main categories: motion, speed, and medium.

Calculating the S-P Interval

One of the most practical applications of understanding these waves is determining the distance to an earthquake's epicenter. Because P waves travel faster than S waves, the time gap between their arrivals (the S-P interval) increases as the waves travel further from the source.

Worked Example: Finding Distance

Imagine a seismograph records the arrival of a P wave at 10:00:00 AM and an S wave at 10:00:30 AM.

1. Calculate the S-P Interval ($\Delta t$):

   \Delta t &= \text{Arrival of S} - \text{Arrival of P} \\ \Delta t &= 30\text{ seconds} \end{aligned}$$ $$$ $$$

2. Use the Distance Formula: While the exact math depends on specific regional velocity models, seismologists use a simplified relationship where distance ($d$) is proportional to the time interval. For many introductory problems, you might use a simplified constant or a travel-time graph.

   If we assume a simplified model where every 1 second of delay equals 8 kilometers of distance:

   d &= \Delta t \cdot 8\text{ km/s} \\ d &= 30 \cdot 8 \\ d &= 240\text{ km} \end{aligned}$$ $$$ $$$

Note: In real-world seismology, the relationship is not a simple linear multiplication because wave speeds change as they pass through different layers of the Earth (like the mantle vs. the crust).

Conclusion

Understanding P and S waves is fundamental to the study of geophysics. By analyzing the speed, motion, and the "shadow zones" created when waves are blocked by liquid layers, scientists can map the invisible interior of our planet. Remember: P waves push, S waves shake, and only S waves stop at liquids.