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WAVES TRAVELLING WAVES TRANSVERSE
AND LONGITUDINAL WAVES |
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Many types of waves can be classified
as transverse
waves or longitudinal (compressional) waves. We will
consider transverse waves in this document. Transverse wave the particles of
the medium vibrate up and down in a direction transverse
(perpendicular) to the motion of the wave. Examples: waves on a stretched string,
electromagnetic waves.
Fig. 1. Transverse wave: the particle marked +
moves up and down executing simple harmonic motion.
The wave advances 1 wavelength in a time
interval of 1 period.
Fig. 2. Animation of a
travelling transverse wave moving to the right.
Each particle executes SHM as they move up and down at right angles
to the propagation direction. Longitudinal (compressional) wave the vibration of the particles of the medium
vibrate along the same direction as the wave is propagating. The wave is characterised by a series of
alternate condensations (compressions) and rarefactions
(expansions). A sinusoidal wavefunction
can also represent a longitudinal wave (figure 4) - the wavefunction gives
the displacement in the direction the wave is travelling. The compressions
correspond to the crests and the rarefactions are the troughs. Example: sound waves in air.
Fig. 3. Longitudinal wave: the particle marked +
moves backward and forward executing simple harmonic
motion. The wave advances 1 wavelength in a time interval of
1 period. The particles oscillate over very small distances, whereas the
wave itself propagates over much larger distances. The wavelength is the
distance between adjacent compressions or between adjacent rarefactions.
Motion along a slinky
Sound wave
generated by a tuning fork
Fig. 4. Sound wave travelling through the air |
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Earthquakes Both transverse and longitudinal waves
are produced when an earthquake occurs. S waves (shear waves) P waves (pressure waves) L waves (surface
waves) travel along the
Earths surface. The motion is essentially elliptical (transverse +
longitudinal). These waves are mainly responsible for the damage caused by
earthquakes.
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Water waves A
water wave is a surface wave that moves along the boundary between the water
and the air. The motion of each water molecule at the surface is elliptical
and so is a combination of transverse and longitudinal motions. Below the
surface, the motion is only longitudinal.
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Tsunami Tsunami is the name given to the very
long waves on the ocean generated by earthquakes or other events which
suddenly displace a large volume of water. "Tsunami" is from
"harbor wave" in Japanese. A tsunami is distinct from ordinary
wind-driven ocean waves in that its source of energy is a water displacement
event. The wave speeds for tsunamis are very
high in deep water. The tsunami of December 26, 2004 travelled from near the
island of Sumatra to the east coast of Africa in just over seven hours. It
was initiated by an earthquake of magnitude 9 off the western coast of
northern Sumatra. The wave speed depends upon wavelength
and the depth of the water for tsunamis at sea. As waves enter shallower
water, their wavelength and wave speed diminishes, causing their amplitudes to
greatly increase. Tsunami waves are distinguished from
ordinary ocean waves by their great length between wave crests, often exceeding
100 km in the deep ocean water, and by the time between these crests, ranging
from 10 minutes to an hour. As they reach the shallow waters of the coast,
the waves slow down and the water can pile up into a wall of destruction tens
of meters or more in height. The effect can be amplified where a bay or
harbour funnels the wave as it moves inland. Large tsunamis have been known
to rise over 30 meters. Even a tsunami 3 - 6 meters high can be very
destructive and cause many deaths and injuries. Some tsunamis consist of a single
crest while others develop a broad trough in advance of the main wave and a
succession of smaller waves behind. It is the preceding trough, together with
man's curiosity, that has been the cause of much loss of life. People attracted
by the very low water as the tsunami approaches have gone out to walk on the
newly exposed sea floor and have been drowned as the rising pulse flooded
shoreward. Depth of water (m) 10 50 200 2000 4000 7000 Velocity (km.h-1 ) 40 80 160 500 700 950 Wavelength (km) 10 20 50 150 200 280 amazing
numbers !!!
Workshop Activity: Graphical Analysis of Travelling Waves Workshop Activity:
Transverse Travelling Waves
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Animation
produced with wm_travelling.m If you have any feedback, comments, suggestions or corrections please email: Ian Cooper
School of Physics University
of Sydney ian.cooper@sydney.edu.au |