The Mathematics of Waves

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# The Mathematics of Waves - PowerPoint PPT Presentation

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

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
• 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
• 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 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 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
• 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 – 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 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 wave
• So we now know that:
• Velocity is in the units m/s
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 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 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
• Pulse Wave
• Periodic Wave
• Crest
• Trough
• Amplitude
• Amplitude and Energy
• Period (T)
• Frequency (f)
• Wavelength (λ)
• Velocity Formula