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The Mathematics of WavesPowerPoint Presentation

The Mathematics of Waves

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The Mathematics of Waves

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The Mathematics of Waves

- As if there weren’t enough categories for types of waves yet…
- We can look at 2 different types of mathematical waves
- Pulse Waves
- Periodic Waves
- Much of this class will look at periodic waves

- A pulse wave is when a single burst of energy is sent through a medium/space
- Imagine having a straight rope and lifting it once to send a ‘pulse’ of energy through the rope

- If it were perfectly silent and someone blasted an air horn for a brief second. This would send a pulse of energy through the air molecules in the room. This would create a single pulse wave that travels through the air
- In a perfectly dark room, if you flicked the lights on and then off for an instant. This would send a pulse of light through the room.

- Periodic waves are when continuous energy is sent through a medium/space
- Imagine shaking the end of a rope up and down, over and over again

- In a mechanical wave, the amplitude is related to the energy carried in the wave
- The energy carried by the wave will be proportional to the amplitude squared
- For Example - Think about creating waves in a rope. If you want to make the waves go higher, you have to work harder (put in more energy)

- This is NOT NECESSARILYTHE CASE FOR
ELECTROMAGNETIC WAVES

- Example
The amplitude of an ocean wave is 2.00 m high. If the wave doubles in height, by what factor does the energy carried by the wave increase?

- Velocity – The velocity (as you learned in grade 10) is the distance travelled divided by the time
- We know that with wave, the distance is measured in wavelengths and the time is measures in periods

- We can re-write that equation such as:
- We also know that 1/T is the frequency of a wave. So we can write:

- So we now know that:
- Velocity is in the units m/s

- Example #1
Yellow light has a frequency of 508 THz. If the yellow light has a wavelength of 570 nm, what is the velocity of yellow light?

- Example #2
The velocity of sound through air is 340 m/s. Middle C on a piano has a frequency of 261.6 Hz. What is the wavelength of middle C?

- Example #3
Blue light has a frequency of 606 THz and a wavelength of 450.0 nm. How long would it take blue light to reach the Earth from the Sun if the Earth is 1.496*108 km away?

- Pulse Wave
- Periodic Wave
- Crest
- Trough
- Amplitude
- Amplitude and Energy
- Period (T)
- Frequency (f)
- Wavelength (λ)
- Velocity Formula