The mathematics of waves
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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 Waves

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The mathematics of waves

The Mathematics of Waves


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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