# The Mathematics of Waves - PowerPoint PPT Presentation

1 / 14

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

The Mathematics of Waves

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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