# Waves

Urban and Civil

Nov 29, 2013 (3 years and 8 months ago)

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Waves

Definition

Mechanical Wave
-

transfer of energy
through a medium

Waves can move over large distances, but
the particles of the medium only vibrate

Waves transport energy but not matter

Mechanical waves must travel through a
medium

Wave Properties

Waves are propagated by a vibrating
source

Pulse

single disturbance created by a
single oscillation

Periodic Wave

periodic disturbance
created by a continuously vibrating source

Types of Waves

Transverse

particles in medium vibrate
perpendicular to the direction of the wave
motion

A

crest

trough

Crest

max displacement

Trough

minimum displacement

λ

wavelength

distance between two
successive crests (or troughs)

A

amplitude

maximum displacement
from the rest position

Longitudinal Waves

Particles vibrate parallel to the direction of
wave motion

compression

rarefaction

Compression

wave particles are
compacted closely together

Rarefaction

out

Wavelength

distance between two
corresponding in phase points

Amplitude

maximum displacement from
rest

Damping

Initial amplitude of the wave depends on
the initial energy of the source

Energy decreases over time, so the
amplitude does as well
-

damping

Wave Equation

The velocity of a wave is related to its
wavelength and frequency

Velocity

speed the wave travels

Frequency

number of cycles that pass a
given point per second (in Hertz)

-

measured by crests per second

v =
λf

Example

A wave has a wavelength of 5m and a
frequency of 3 Hz. What is its speed?

A crest of a wave in a pool takes 2.5sec to
travel from one end to the other end (20m).
It is noticed that 10 crests pass by a mark
in 15 sec. What is the wavelength?

The frequency of a wave is determined by
the rate that the source produces them

The velocity of a wave depends on the
properties of the medium

Velocity of Transverse

In transverse waves the velocity depends
on the tension (tightness) of the medium
and the mass/length of the medium

Greater tension increase both v and f

v =
√(F
t
/(m/L))

Example

A wave of wavelength .30m is traveling
down a 300m long wire of mass 15kg. If
the wire is under a tension of 1000N, what
is the velocity and frequency of the wave?

Longitudinal Velocity

Velocity in longitudinal waves depends on
the elasticity(E) of the material and the
density(
ρ)

of the material

v =
√(E/ ρ)

Example

You can hear a train approaching by
putting your ear to the track. How long
does it take for a sound wave to travel
1.0km down a steel track?
E = 2.0x10
11

N/m
2
and
ρ = 7.8x10
3

kg/m
3