Nats 101 S04 #12
Reading: T&H 141-149
Energy can travel in two ways: by particle or by wave. E.g. dominoes
Properties of waves: wavelength, frequency, velocity, amplitude
n = l w
2 kinds of waves, transverse and longitudinal, examples
limits of human hearing
constructive and destructive interference
Energy transfer by waves
In our last lectures we discussed the nature of magnetism and electricity, and introduced the concept of an energy field.
Now we will discuss how energy can be transported.
This is not about how it is converted to another form, simply how it gets
from point a to point b.
Energy can travel in one of two ways. By particle or by wave. Now remember
that the way I was picturing the nature of the universe, matter and all,
was by describing it as a distortion of space. The form of the distortion
can be described mathematically in terms of waves. If the wave is a standing
wave then the form is matter. If the wave is travelling then it is radiation.
Let us discuss the general nature of waves and energy transfer.
A classic example of energy transfer is summed up in the statement: “They
went down like a row of dominoes”. What does this mean?
Suppose we wanted to knock down a standing domino. Then we could do it by
a) throwing another domino at it with enough kinetic energy to knock
b) We could also do it by setting up a row of dominoes, and knocking
the 1st one over, which hits the 2nd etc, until it hits the domino that
you wanted to knock over.
The 1st way is an example of energy traveling by particle, and the second
is an example of energy travelling by wave. We started a wave of falling
A wave can be defined as a travelling disturbance. It carries energy from
one point to another, without requiring matter to travel between the points.
The properties of waves
A classic image of a wave is the ripple produced by throwing a rock into
a pond. Let’s analyze the shape of the wave. Four measurements completely
characterize the wave.
1. Wavelength: The distance between crests
2. Frequency: The number of wave crests that pass a point
every second. If one wave goes by you every second then we say that the
frequency is 1 cycle per sec or 1 hertz (Hz).
3. Velocity: the speed and direction that the wave crest
itself is moving. E.g. ocean waves travel a few meters per sec. (6 miles/hour).
E.g. sound travels in air around 340 m/sec = 1100 ft/sec = 750 miles/hour.
Note that the speed of sound varies from one material to another. We will
talk about what sound is later.
4. Amplitude: The height of the wave crest above the
The relationship between wavelength, frequency, and velocity
n = l w
There is a simple relationship between the wavelength (l),
frequency (w), and velocity (n).
If you know any 2 of them then you can compute the 3rd using
or, velocity (n) equals wavelength (l)
times frequency (w).
The logic is straight forward. For example, ocean waves: if the wave crests are 6 m apart, and there is one wave per every
2 sec, then the wave must be travelling
= lw = 6 m/2 sec = 3 m/sec.
Two kinds of waves: transverse and longitudinal
Suppose a piece of wood is floating on the surface of a pond. You throw
a rock into the pond and create a ripple of waves. The waves move outwards
from where the rock hit. When the waves pass the wood, it bobs up and down.
The wood does not move in the same direction as the wave is moving, but
rather it moves in a direction perpendicular to the travel of the wave,
In the case of the falling dominoes, the movement of the dominoes was in
the direction parallel to the movement of the wave, i.e. longitudinal.
Sound waves are longitudinal. When we speak, the vocal cords vibrate the
air, setting it into motion. The molecules of air vibrate in the same direction
as the vibration of your vocal cords. These molecules in turn vibrate the
molecules next to them, and so on. The region in which the molecules get
pushed becomes more dense then the region around it, because more
molecules are there. The increased density pushes these neighboring molecules
further ahead and the sound travels. This sort of longitudinal wave is also called a
pressure or compression wave.
Earthquakes can also be compression waves. One of the things that I study
is to compress crystals and see how the atoms respond. The ease in which
a material can be compressed is related to the speed in which sound waves
can travel through it. For instance, diamond is very incompressible, and
sound waves, or compression waves, travel through it very fast.
The speed of sound in air varies depending upon the temperature or density
of the air. Hot air has lower density and therefore sound travels slower.
Sound travels faster through cold air.
Amplitude is not tied into the equation relating the other 3 wave parameters.
It can be anything it wants to be. The amplitude of a sound
wave is how loud the sound is. The unit of measurement for the amplitude of a sound wave is called decibels.
For an earthquake, the Richter scale measures
the amplitude. The greater the amplitude the greater the displacement of
the earth, and the greater the damage.
The limits of human hearing
The human ear hears sounds in the range of 20 – 20,000 Hz,
i.e. 20 – 20 kHz. This range can be converted to wavelengths (by l
= n / w = 1100 ft/sec / 20 Hz =) 55 ft long at 20 Hz to 2/3 inch
long at 20 kHz.
Frequencies lower than 20 Hz are felt rather than heard. E.g. the mating
call of the female elephant is not heard by human, but rather it is felt.
Our perception of our own voice is always "fuller" than a recording,
because when we speak we also transmit low frequency waves through our bone
structure. A recording does not include these low frequencies.
If you have been to many rock concerts then you are familar with two frequencies that
are indicators of electronic problems. These frequencies are 60 Hz and 120 Hz. The 60 Hz
signal is the same as the AC current frequency and indicates a grounding problem.
The 120 Hz signal is a result of rectifying the 60 Hz signal and indicates a power supply problem.
to hear computer generated frequencies. This might be too difficult to
do until after a demonstration by Dr Downs.
Suppose two rocks hit the pond at the same time. Then waves would be produced
by both. According to a concept called the superposition principle,
the displacement of water at any given point is the sum of the
contribution from each set of waves. The net effect is called interference.
Two extremes are possible, with anything in between.
If both sets of waves meet at their crest, then the resulting amplitude
will be the sum of both. E.g., if both amplitudes were 1 ft.high , then
the result would be a point that is 2 ft high. This is called constructive
At the same time, somewhere else, the crest of one wave is meeting the
bottom of the other. The result is as if no wave were present. This is
called destructive interference. This can happen in a poorly
designed auditorium for instance. There may be seats in which the sound
quality is low. It is usually a function of frequency.
At my old house I could play "Dark Side of the Moon", and there were certain
notes that resonated at a certain spot in one of the bedrooms. It was
the only note that I would hear there, and the volume would vary depending
upon exactly where I was standing.
to see a computer generated image. http://webphysics.davidson.edu/WebTalks/Applets/Applets.html