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The Mathematics of Waves. 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. Pulse Waves.

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the mathematics of waves1
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
pulse waves
Pulse 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
real life examples of pulse waves
Real Life Examples of pulse waves
  • 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
Periodic Waves
  • 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
the mathematics of waves2
The Mathematics of Waves
  • 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

energy of a wave
Energy of a Wave
  • 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 of a wave
Velocity of a wave
  • 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
velocity of a wave1
Velocity of a wave
  • We can re-write that equation such as:
  • We also know that 1/T is the frequency of a wave. So we can write:
velocity of a wave2
Velocity of a wave
  • So we now know that:
  • Velocity is in the units m/s
velocity of a wave3
Velocity of a wave
  • 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?

velocity of a wave4
Velocity of a wave
  • 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?

velocity of a wave5
Velocity of a wave
  • 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?

what you should know
What you should know
  • Pulse Wave
  • Periodic Wave
  • Crest
  • Trough
  • Amplitude
  • Amplitude and Energy
  • Period (T)
  • Frequency (f)
  • Wavelength (λ)
  • Velocity Formula
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