Quick notes for 11-9 through 11-12
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Energy is transported by waves. The medium doesn’t move forward the energy does --from particle to particle.
When energy is transported by a wave, Energy is proportional to the square of the amplitude
Intensity (I) of the wave is defined as the power (energy/time) / area it is transported across
Intensity is measure in Watts/m2
Intensity is also proportional to the amplitude squared
A spherical wave is one that moves out in all directions and as it moves it is spread over a larger and larger area.
this area is a sphere and therefore is equal to 4r2, so that I=Power/4r2
Inverse Square Law states that the Intensity is inversely proportional to r2 and therefore if you compare the
intensity going outward if the distance double the intensity is reduced by ¼
Amplitude also decreases with distance, and is inversely proportional to r, so that if distance is doubled the
amplitude it ½.
The above are only for spherical waves and not one dimensional, where amplitude and intensity do not decrease
over distance..
We can calculate in a SHM the energy that passes each particle. E=1/2 kA2
We can rewrite this in terms of frequency E=22mf2A2
we can then substitute mass by using m=V -- is the density of the medium and V is the volume of the medium
and then substitute S l for V – S is th e surface area of the medium and l is the distance the wave travels. and
finally substitute vt for l to finally get E=22Svf2A2.
From the above equation you can also calculate both power and intensity (see pg 311)
Reflection and Transmission of waves
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A wave that reaches the end of its medium will reflect part of the wave back.
If the medium changes, part is reflected back and part will continue to transmit.
The denser the medium, the more that is reflected back and the less that is transmitted.
Wave fronts are the points along the wave forming the wave crest (seashore wave)
A ray is a line drawn in the direction of wave motion perpendicular to the wave front.
Plane waves are waves far from their source and so the wave fronts are no longer curved.
Law of reflection is that the angle of reflection equals the angle of incidence. The angle of incidence is defined
as the angle the incident ray makes perpendicular to the surface.
Interference:
1. Interference occurs when two waves pass through the same region of space at the same time.
2. Where waves overlap, the resultant displacement is the algebraic sum of their separate displacements, this is
called the principle of superposition.
3. Destructive displacement is when two waves have opposite displacements and so they add up to 0-in other
words they cancel each other out.
4. Constructive interference is when two waves produce a resultant displacement that is larger than either wave.
5. Phase is the relative position of waves crest, in phase is constructive displacement, out of phase is destructive.
Standing Waves: Resonance
1. A standing wave can be produced by using a cord that has one fixed end and the shaken. The wave will be
reflected back and waves will travel in both directions.
2. If the oscillations are at the right frequency the two traveling waves will interfere so that a larg amplitude
standing wave is a result.
3. Points of destructive interference, where the cord appears not to move are called nodes.
4. Points of constructive interference are called antinodes.
5. Resonant frequencies are the frequencies that standing waves are produced.
6. Standing waves are a vibrating object at resonance.
7. Cords can have many resonant frequencies.
8. Lowest frequency is called the Fundamental frequency
9. Overtones is the term for other natural frequencies
10. Harmonics is the term for overtones on a vibrating sting and the first harmonic is the fundamental frequency.
11. Each continuing harmonic is named in order and is a portion of the wavelength. (2nd harmonic is one full
wavelength)