Longitudinal Waves
Ck12 Science
Say Thanks to the Authors
Click http://www.ck12.org/saythanks
(No sign in required)
To access a customizable version of this book, as well as other
interactive content, visit www.ck12.org
CK-12 Foundation is a non-profit organization with a mission to
reduce the cost of textbook materials for the K-12 market both
in the U.S. and worldwide. Using an open-content, web-based
collaborative model termed the FlexBook®, CK-12 intends to
pioneer the generation and distribution of high-quality educational
content that will serve both as core text as well as provide an
adaptive environment for learning, powered through the FlexBook
Platform®.
Copyright © 2013 CK-12 Foundation, www.ck12.org
The names “CK-12” and “CK12” and associated logos and the
terms “FlexBook®” and “FlexBook Platform®” (collectively
“CK-12 Marks”) are trademarks and service marks of CK-12
Foundation and are protected by federal, state, and international
laws.
Any form of reproduction of this book in any format or medium,
in whole or in sections must include the referral attribution link
http://www.ck12.org/saythanks (placed in a visible location) in
addition to the following terms.
Except as otherwise noted, all CK-12 Content (including
CK-12 Curriculum Material) is made available to Users
in accordance with the Creative Commons Attribution/NonCommercial/Share Alike 3.0 Unported (CC BY-NC-SA) License
(http://creativecommons.org/licenses/by-nc-sa/3.0/), as amended
and updated by Creative Commons from time to time (the “CC
License”), which is incorporated herein by this reference.
Complete terms can be found at http://www.ck12.org/terms.
Printed: August 20, 2013
AUTHOR
Ck12 Science
www.ck12.org
C ONCEPT
Concept 1. Longitudinal Waves
1
Longitudinal Waves
• Describe longitudinal waves.
Longitudinal waves are a series of compressions and rarefactions (expansions).
A longitudinal wave can be generated in a spring by pushing the hand forward creating a compression and then
pulling the hand backward creating a rarefaction or expansion. If this process is continued, a longitudinal wave train
is produced.
1
www.ck12.org
Longitudinal Waves
Longitudinal waves cause the particles of medium to move parallel to the direction of the wave. Longitudinal
waves are created in springs by pushing and pulling the spring in the same direction as the motion of the wave. A
sound wave is another example of longitudinal waves.
In springs or in air, pushing the media closer together produces a compression (an area of higher density) and pulling
the media further apart creates a rarefaction (an area of lower density).
Fluids (liquids, gases, plasmas) usually transmit only longitudinal waves. (Although the surface waves on water are
transverse.)
The wavelength of longitudinal waves is measured by the distance separating the densest compressions. The
amplitude of longitudinal waves is the difference in media density between the undisturbed density to the highest
density in a compression.
2
www.ck12.org
Concept 1. Longitudinal Waves
Example Problem: A sonar signal (sonar is sound waves traveling through water) of 1.00 × 106 Hz frequency has
a wavelength of 1.50 mm in water. What is the speed of sound in water?
Solution: v = λ f = (0.00150 m)(1.00 × 106 s−1 ) = 1500 m/s
Example Problem: A sound wave of wavelength 0.70 m and velocity 330 m/s is produced for 0.50 s.
a. What is the frequency of the wave?
b. How many complete waves are emitted in this time interval?
c. After 0.50 s, how far is the wave front from the source of the sound?
Solution:
m/s
−1
a. f = λv = 330
0.70 m = 470 s
b. complete waves = (470 cycles/s)(0.50 s) = 235 cycles
c. distance = (330 m/s)(0.50 s) = 115 m
Summary
• Longitudinal waves cause the particles of medium to move parallel to the direction of the wave.
Practice
http://www.youtube.com/watch?v=bomzzHC-59k
1. What sound producing object is discussed in the video?
2. What are the crests and troughs for sound waves?
3. What work is mispronounced by the narrator in the video?
Review
1. Some giant ocean waves have a wavelength of 25 m are and travel at speeds of 6.5 m/s. Determine the
frequency and period of such a wave.
3
www.ck12.org
2. Bats use sound echoes to navigate and hunt. The emit pulses of high frequency sound waves which reflect off
obstacles in the surroundings. By detecting the time delay between the emission and return of a pulse, a bat
can determine the location of the object. What is the time delay between the sending and return of a pulse
from an object located 12.5 m away. The approximate speed of sound is 345 m/s.
3. Sachi is listening to her favorite radio station which broadcasts radio signals with a frequency of 1.023 ×
108 Hz. If the speed of the signals in air is 2.997 × 108 m/s, what is the wavelength of these radio signals.
4. A longitudinal wave is observed to be moving along a slinky. Adjacent crests are 2.4 m apart. Exactly 6
crests are observed to move past a given point in 9.1 s. Determine the wavelength, frequency, and speed of
this wave.
5. A sonar signal leaves a submarine, travels through the water to another submarine and reflects back to the
original submarine in 4.00 s. If the frequency of the signal was 512 cycles per second and the wavelength of
the signal was 2.93 m, how far away is the second submarine?
• longitudinal wave: A wave in which the direction of media displacement is the same as the direction of wave
propagation.
References
1.
2.
3.
4.
4
CK-12 Foundation - Samantha Bacic. . CC-BY-NC-SA 3.0
CK-12 Foundation - Christopher Auyeung. . CC-BY-NC-SA 3.0
CK-12 Foundation - Samantha Bacic. . CC-BY-NC-SA 3.0
CK-12 Foundation. . CCSA