Ch. 15 - Wave Motion

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 15 - Wave Motion

Problem 17a

Chapter 15, Problem 17a

What is the ratio of the intensities, of an earthquake P wave passing through the Earth and detected at two points 15 km and 55 km from the source?

Verified step by step guidance

Understand that the intensity of a wave decreases as it propagates through a medium. For a spherical wave, the intensity is inversely proportional to the square of the distance from the source. This relationship can be expressed as \( I \propto \frac{1}{r^2} \), where \( I \) is the intensity and \( r \) is the distance from the source.

To find the ratio of intensities at two distances, \( r_1 \) and \( r_2 \), use the formula: \( \frac{I_1}{I_2} = \frac{r_2^2}{r_1^2} \). Here, \( I_1 \) and \( I_2 \) are the intensities at distances \( r_1 \) and \( r_2 \), respectively.

Substitute the given distances into the formula. Let \( r_1 = 15 \ \text{km} \) and \( r_2 = 55 \ \text{km} \). The ratio becomes \( \frac{I_1}{I_2} = \frac{55^2}{15^2} \).

Simplify the expression for the ratio by calculating the squares of the distances: \( \frac{I_1}{I_2} = \frac{3025}{225} \).

Conclude that the ratio of the intensities is determined by dividing the two values obtained in the previous step. This gives the final ratio of intensities at the two points.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

P Waves

P waves, or primary waves, are a type of seismic wave that compress and expand the material they travel through. They are the fastest seismic waves and can move through solids, liquids, and gases. Understanding P waves is crucial for analyzing how seismic energy propagates through the Earth and how it is detected at various distances from the source.

Intensity of Seismic Waves

The intensity of seismic waves refers to the energy carried by the waves as they travel through the Earth. It is typically measured in terms of amplitude and is influenced by the distance from the source, the medium through which the waves travel, and the wave type. The intensity decreases with distance, which is essential for calculating the ratio of intensities at different points from the earthquake source.

Inverse Square Law

The inverse square law states that the intensity of a physical quantity (like light or seismic waves) decreases with the square of the distance from the source. This principle is fundamental in understanding how the intensity of seismic waves diminishes as they propagate through the Earth, allowing for the calculation of intensity ratios at different distances from the earthquake's epicenter.

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