#### Introduction

- Sound is defined as an alteration in pressure which moves through an elastic medium such as air.
- It is transmitted through the medium as a wave and is therefore called a sound wave.
- Sound waves are an example of longitudinal waves.

#### Spherical Waves

- One of the simplest sound waves is produced from popping a balloon.
- In the interactive demonstration below, try moving the time slider and see how the pressure changes as the balloon pops.

- At time 0:
- The balloon hasn't popped
- The pressure inside the balloon is higher than the normal atmospheric pressure

- Once the balloon has popped:
- The pressure that was inside the balloon radiates outwards as a pulse of pressure
- If you look at the pressure pulse you will see it is formed of two parts:
- First, the pressure increases above the normal level. This is called the condensation pulse
- Then, the pressure drops below the normal level. This is called the rarefaction pulse

- Also notice that the height of the wave decreases as it moves further away from the center
- This is because the magnitude of the wave is inversely proportional to the distance from its source.

- This type of sound wave is called a "spherical wave".
- Spherical waves propagate outwards in all directions.

#### Plane Wave

- Plane waves are different from spherical waves in that they only propagate in a single direction.

#### Cycle

- A cycle is a set of pressure variations that start and end at the same condition.

#### Phase

- A phase is a specific point in a cycle.

- In the above example, the red lines represent phases in the cycle.
- Phases are described as an angle, with the entire cycle spanning 360°.
- Phase can also be used to describe the shift between two otherwise identical waves:

- The two waves above are identical apart from the phase. The phase between these two waves is 45°.

#### Speed

- Technically referred to as the "velocity of the propagation of the wave".
- There are 3 factors that affect the velocity:
- γ = the heat capacity ratio of the gas
- p
_{0}= the static pressure in the gas, measured in dynes per square centimeter - ρ = the density of the gas, measured in grams per square centimeter

- Then the speed, measured in centimeters per second is:
- As the pressure increases, the density also increases. This means that a change in pressure doesn't affect the speed of the wave.
- Therefore the speed of the wave can be expressed only in terms of temperature.
- The speed of a sound wave, in air, measured in centimeters per second is: where t = the temperature in degrees centigrade.

#### Frequency

- A sound wave can contain a single cycle, but it is often formed from multiple repeating cycles.
- The number of cycles in a single second is called the frequency.
- Frequency is measured in hertz (Hz). 1Hz is one cycle per second.

#### Wavelength

- the wavelength is simply the distance a wave travels to complete one cycle.
- This is related to the frequency of the wave and the speed that it travels:
- c = the speed of the wave.
- λ = the wavelength of the wave.
- f = the frequency of the wave.

#### Pressure

- A sound wave is a pressure wave.
- It consists of pressures above and below the normal pressure of the gas.
- Instantaneous sound pressure:
- This is the pressure at a given point in the wave, minus the normal pressure of the gas.
- It is the change in pressure caused by the wave.

- Effective sound pressure
- This is the Instantaneous sound pressure over a complete cycle as the wave passes over a given point.
- It is expressed as a single value by finding the root mean square of the complete cycle.
- It is measured in dynes per square centimeter.
- It is often shortened to "sound pressure".