• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

11-39P

Expert-verified
Physics Principles with Applications
Found in: Page 292
Physics Principles with Applications

Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

P and S waves from an earthquake travel at different speeds, and this difference helps locate the earthquake “epicenter” (where the disturbance took place). (a) Assuming typical speeds of and for P and S waves, respectively, how far away did an earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.5 min apart? (b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

(a) The earth quake occurs at a distance of \(1400\;{\rm{km}}\) from a seismic station.

(b) No, one seismic station is not enough in order to find the epicenter. Through one seismic station, only distance can be known and one cannot identify the direction of an earthquake. So, data from two to three other stations is necessary for the correct position of the epicenter.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Understanding about the distance

Whenever a particle moves with a specific speed in a particular direction, then the particle would cover the distance that varies with the values of time and speed. The relation between distance and time taken by the particle is linear.

Identification of given data

The given data can be listed below as,

  • The typical speed of \(P\) wave is \({v_1} = \left( {8.5\;{\rm{km/s}}\; \times \frac{{{{10}^3}\;{\rm{m/s}}}}{{1\;{\rm{km/s}}}}} \right) = 8.5 \times {10^3}\;{\rm{m/s}}\).
  • The typical speed of \(S\) wave is\({v_2} = \left( {5.5\;{\rm{km/s}}\; \times \frac{{{{10}^3}\;{\rm{m/s}}}}{{1\;{\rm{km/s}}}}} \right) = 5.5 \times {10^3}\;{\rm{m/s}}\).
  • The time lag between the arrival of the two waves is \(t = 1.5\;\min \).

Determining the relation between velocity and time of both waves

(a) Since, the distance traveled by the both waves is same, then the expression of the distance traveled by the both waves can be represented as,

\(\begin{aligned}{c}\Delta {x_1} = \Delta {x_2}\\{v_1}{t_1} = {v_2}{t_2}\end{aligned}\)

Here, \({t_1}\) and \({t_2}\) are the time taken by both waves \(\left( P \right)\) and \(\left( S \right)\) respectively.

As the time taken by the \(S\) wave will be more when compared to that of the \(P\) wave as the speed of the \(S\) wave is less when compared to that of the \(P\) wave then the time lag between the arrival of the two waves can be represented as,

\(\begin{aligned}{c}{t_2} - {t_1} &= \left( {1.5\;\min \; \times \frac{{60.0\;\sec }}{{1\;\min }}} \right)\\{t_2} - {t_1} &= 90.0\;\sec \\{t_2} &= \left( {{t_1} + 90.0\;\sec } \right)\end{aligned}\)

Determining the time taken by the both waves

Substitute all the known values in the above expression of distance travelled by both waves.

\(\begin{aligned}{c}\left( {8.5 \times {{10}^3}\;{\rm{m/s}}} \right){t_1} &= \left( {5.5 \times {{10}^3}\;{\rm{m/s}}} \right)\left( {90.0\;{\rm{s}} + {t_1}} \right)\\8.5{t_1} &= 495 + 5.5{t_1}\\3{t_1} &= 495\;{\rm{s}}\\{t_1} &= 165\;{\rm{s}}\end{aligned}\)

The value of \({t_2}\) can be calculated with the help of known values as,

\(\begin{aligned}{c}{t_2} &= \left( {{t_1} + 90\;{\rm{s}}} \right)\\ &= \left( {165\;{\rm{s}}\;{\rm{ + }}\;{\rm{90}}\;{\rm{s}}} \right)\\ &= 255\;{\rm{s}}\end{aligned}\)

Determining the distance travelled by the waves

The expression of the distance travelled by the waves can be calculated as,

\(\begin{aligned}{c}\Delta {x_1} &= {v_1}{t_1}\\ &= \left( {8.5 \times {{10}^3}\;{\rm{m}}/{\rm{s}}} \right)(165\;{\rm{s}})\\ &\approx \left( {1.40 \times {{10}^6}\;{\rm{m}}} \right)\left( {\frac{{1.0\;{\rm{km}}}}{{{{10}^3}\;{\rm{m}}}}} \right)\\ &\approx 1400\;{\rm{km}}\end{aligned}\)

Thus, the distance travelled by the both the waves is \(1400\;{\rm{km}}\).

Determining whether one station is sufficient or not to determine epicenter.

(b) No, one seismic station is not enough in order to find the epicenter. Only distance can be known through one seismic station, and one cannot identify the direction of an earthquake. So, data from two to three other stations is necessary for the correct position of the epicenter.

Most popular questions for Physics Textbooks

One end of a horizontal string is attached to a small amplitude mechanical 60.0-Hz oscillator. The string’s mass per unit length is\({\bf{3}}.{\bf{5}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{4}}}}{\rm{ }}{\bf{kg}}{\rm{/}}{\bf{m}}\). The string passes over a pulley, a distance \({\bf{l}} = {\bf{1}}.{\bf{50}}{\rm{ }}{\bf{m}}\) away, and weights are hung from this end, Fig. 11–55. What mass m must be hung from this end of the string to produce (a) one loop, (b) two loops, and (c) five loops of a standing wave? Assume the string at the oscillator is a node, which is nearly true.

A guitar string is 92 cm long and has a mass of 3.4 g. The distance from the bridge to the support post is \({\bf{l}} = {\bf{62}}{\rm{ }}{\bf{cm}}\), and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?

The intensity of an earthquake wave passing through the Earth is measured to be \(3.0 \times 1{0^6}\;J/{m^2}\) at a distance of 54 km from the source. (a) What was its intensity when it passed a point only 1.0 km from the source? (b) At what rate did energy pass through an area of \(2.0\;{m^2}\)at 1.0 km?

What is wrong with this road sign:

Memphis 7 mi (11.263 km)?

Multiply \({\bf{3}}{\bf{.079 \times 1}}{{\bf{0}}^{\bf{2}}}{\bf{ m}}\) by \({\bf{0}}{\bf{.068 \times 1}}{{\bf{0}}^{{\bf{ - 1}}}}{\bf{ m}}\), taking into account significant figures.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Physics of Motion

Read explanation

Scientific Method Physics

Read explanation

Famous Physicists

Read explanation

Fluids

Read explanation

Torque and Rotational Motion

Read explanation

Nuclear Physics

Read explanation

Fields in Physics

Read explanation

Measurements

Read explanation

Space Physics

Read explanation

Electricity

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Electrostatics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Mechanics and Materials

Read explanation

Engineering Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Particle Model of Matter

Read explanation

Waves Physics

Read explanation

Magnetism

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Linear Momentum

Read explanation

Rotational Dynamics

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Geometrical and Physical Optics

Read explanation

Thermodynamics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Electric Charge Field and Potential

Read explanation

Turning Points in Physics

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.