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 3b

Chapter 15, Problem 3b

Calculate the speed of longitudinal waves in granite, using Tables in Chapters 12 and 13.

Verified step by step guidance

Identify the formula for the speed of longitudinal waves (sound waves) in a solid material. The formula is:

v = \sqrt{\frac{K}{ρ}}

, where

K

is the bulk modulus of the material and

ρ

is the density of the material.

Refer to the tables in Chapters 12 and 13 to find the bulk modulus (

K

) and density (

ρ

) of granite. For example, the bulk modulus of granite might be approximately

4.5 \times 10^{10} Pa

, and its density might be around

2700 kg / m^{3}

Substitute the values of

K

and

ρ

into the formula. For example:

v = \sqrt{\frac{4.5}{\times}}

Simplify the expression under the square root to calculate the ratio of the bulk modulus to the density. This step involves dividing the bulk modulus by the density.

Take the square root of the result from the previous step to find the speed of longitudinal waves in granite. Ensure the units are consistent, and the final speed is expressed in meters per second (m/s).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Longitudinal Waves

Longitudinal waves are waves in which the particle displacement is parallel to the direction of wave propagation. In these waves, compressions and rarefactions move through the medium, allowing energy to transfer without the bulk movement of matter. Sound waves in air and seismic P-waves are common examples of longitudinal waves.

Wave Speed Calculation

The speed of a wave is determined by the properties of the medium through which it travels. For longitudinal waves, the speed can be calculated using the formula v = √(E/ρ), where E is the modulus of elasticity (or bulk modulus) and ρ is the density of the material. This relationship highlights how both the stiffness and density of a medium influence wave speed.

Material Properties of Granite

Granite is an igneous rock composed mainly of quartz, feldspar, and mica, characterized by its density and elasticity. The specific values for the bulk modulus and density of granite are essential for calculating the speed of longitudinal waves in this material. Understanding these properties allows for accurate predictions of wave behavior in geological contexts.

Recommended video:

Guided course

08:45

Properties of Cyclic Thermodynamic Processes

Related Practice

Textbook Question

A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 2.4 s later. How deep is the ocean at this point? (Use Tables 12–1 and 13–1.)

812

views

Textbook Question

A 0.40-kg cord is stretched between two supports 8.7 m apart. When one support is struck by a hammer, a transverse wave travels down the cord and reaches the other support in 0.85 s. What is the tension in the cord?

1183

views

Textbook Question

A ski gondola [pronounced gon–do–la] is connected to the top of a hill by a steel cable of length 710 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a transverse wave pulse along the cable. It is observed that it took 17 s for the pulse to return. What is the tension in the cable?

1062

views