# Sound Waves

### Sound Waves

#### 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
• p0 = 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".