Waves

cypriotcamelUrban and Civil

Nov 29, 2013 (3 years and 6 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
about fixed positions


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


where particles are spread
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