Domanda del libro di testo
Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is carrying 3.5 times the energy. What is the ratio of the amplitudes of the two waves?
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Ch. 15 - Wave Motion
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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TOC.tableOfContents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 15, Problema 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?
Guida verificata passo dopo passo1
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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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.
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Percorso guidato
02:32
Wave Intensity
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.
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Percorso guidato
02:32Wave Intensity
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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Percorso guidato
05:26The Inverse-Square Law for Intensity
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