A wave is the transmission of energy through a medium. It's a perturbation travelling in a medium. As a matter of fact, a disturbance in the medium occurs as energy moves through it and the first distinction between waves can be made by thinking to the kind of disturbance perturbing the medium:
We have a LONGITUDINAL WAVE if the perturbation is parallel to the velocity of the wave in itself.
We have a TRANSVERSE WAVE if the disturbance perturbs the medium perpendicularly to the velocity of the wave.
(See the figure 15.3 in the textbook on page 294)
When a wave repeats itself at regular interval of time, the whole phenomenon can be resumed by three fundamental quantities:
The wavelength l (lambda) is the distance between same points on different waves. Its unit of measurement is meter (m).[See the figure 15.4 and 15.6 on page 295/296 on the text].
The Period 'T' is the interval of time between the passage of a given wave and the successive one. Its unit of measurement is second (s).
The frequency 'f' is the reciprocal of the period 'T', that means:
f=
1
T
Its unit of measurement is the reciprocal of the second (1/s) and this unit is called Hertz:
1Hz=
1
s
From the physical point of view, the frequency represents the number of oscillations per second the wave performs.
The velocity of a periodic wave can be expressed by the previous quantities. It's just the product of frequency and wavelength of the wave:
v=f·l =
l
T
In a given medium the velocity of the waves is constant and remains always the same. The value of such a velocity depends only on the physical features of the medium.
For example the waves produced on a rope have always the same velocity. This velocity depends on the tension and on the mass per unit length of the rope. Shortly:
v=
æ Ö
F
m
Where 'F' is the magnitude of the tension in the rope and m (mu) is the mass per unit length of the rope:
m =
mass of the rope
length of the rope
=
M
L
.
Since the velocity in a given medium is equal for all the waves in that medium, the relation v=f·l shows that a given frequency will determine the wavelength and viceversa. Lower frequencies give rise to longer wavelength, while higher frequencies result in shorter wavelength (see the sample exercise on page 297 in the text-book).
Interference is the combining, the superposition of two or more waves.
/bf In many processes two or more waves combine (think for instance to the sea waves); the result is a new wave, equal to the sum of the individual waves. This is a general statement known as 'principle of superposition'. The diagrams below show the resulting wave due to the sum of two harmonic waves in four different situations (harmonic waves are waves with a sinusoidal form that can be described by functions sine and cosine).
In the diagram above two sinusoidal waves with amplitude A and B are moving in the same way at the same time . The two waves are completely in phase and get a complete addition resulting in a new wave with amplitude A+B (constructive interference).
The diagram below shows the same interference in the case of two waves having the same amplitude A. The resulting wave has amplitude 2A.
The figure below shows two waves with same amplitude A but completely out of phase:
the sum is always zero and no wave propagates (destructive interference).
Finally, the last diagram shows two waves not completely in phase: their interference gives rise to a new wave with amplitude smaller than 2A.
How does two waves moving in opposite direction interfer? They interfer in a way that produce a fixed standing waves.[read the details on page 299 in the text book]
A good dynamic example showing the standing waves phenomenon can be found at:
http://www.phy.ntnu.edu.tw/java/waveSuperposition/waveSuperposition.html
.
Standing waves are a very common phenomenon. For instance the waves generated by plucking a guitar's string are reflected back and forth on the string producing many standing waves. Each standing wave on the string has a wavelength and a frequency:
l = [ 2L/n] with 'n'=1,2,3,... and where 'L' is equal to length of the string
f=[ v/(l)]=n[ v/2L] where 'v' is the velocity of waves
In particular the main of these standing waves, called fundamental harmonic (n=1) , has a wavelength that is twice the lenght of the string.
l = 2L
The frequency of the fundamental harmonic is related to the musical pitch (altezza della nota musicale) that we hear, and its value is:
f=
v
l
=
v
2L
Then we have the second harmonic (n=2) with wavelength and frequency equal to:
l = L and f=[ v/(l)]=[ v/L]
the third harmonic (n=3) with wavelength and frequency equal to:
l = [ 2L/3] and f=[ v/(l)]=[ 3v/2L]
and so on...
In other terms, the sound produced by plucking a string is the result of the superposition of the fundamental harmonic and further harmonics whose frequency is multiple of the fundamental one as shown in the figure above.
[Try the sample exercise on page 300 in the text book]
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