Velocity
Velocity describes how quickly sound waves travel through a medium, such as air.
What is Velocity?
Velocity refers to the speed at which a sound wave propagates through a medium. In air, sound waves are longitudinal waves, meaning that the particles in the medium vibrate parallel to the direction that the wave is traveling in. The velocity of sound is determined by the properties of the medium it is traveling through.
Measuring Velocity:
The velocity of sound in air at 20°C (68°F) is approximately:
344 metres per second (m/s)
1130 feet per second (ft/s)
To calculate velocity, we use this formula:
Velocity = Distance / Time
Where:
Velocity is in m/s or ft/s
Distance is in metres or feet
Time is in seconds
For example, if a sound wave travels 2260 ft in 2 seconds, its velocity is:
Velocity = 2260 ft / 2s = 1130 ft/s
Factors affecting Velocity:
Temperature: Velocity increases as temperature increases. In air, velocity increases by:
(1.1 ft/s (0.306m) for every 1°F increase
(2 ft/s (0.61m) for every 1°C increase
Medium Density: Velocity is inversely related to the square root of the medium’s density. Sound travels faster in less dense mediums.
Elasticity: Velocity is directly related to the square root of the medium’s elasticity. More elastic mediums allow sound to travel faster.
Figure showing the relationship between velocity, distance and time.
Compression and Rarefaction
In sound waves, compression and rarefaction refer to the two alternating states of the medium particles as the wave propagates through it.
Compression: A compression is a region in the medium where the particles are pushed closer together, creating a high-pressure area. As the sound wave travels, it causes the particles to compress in the direction of the wave motion. This is represented by the crests (peaks) of the sound wave.
Rarefaction: A rarefaction is a region in the medium where the particles are pulled apart, creating a low-pressure area. As the sound wave travels, it causes the particles to spread out in the opposite direction of the wave motion. This is represented by the troughs (valleys) of the sound wave.
Compression and Rarefaction in sound waves
Formula:
Here is an example of how velocity of sound air changes with temperature.
v = 1130 + 1.1(T - 68), where v is in ft/s and T is in °F
This formula is used when the temperature is measured in degrees Fahrenheit (°F). Here's what each part means:
1130 is the velocity of sound in air at 68°F (20°C) in ft/s.
1.1 is the increase in velocity (in ft/s) for each degree Fahrenheit above 68°F.
(T - 68) calculates how many degrees above or below 68°F the temperature is.
So, if the temperature is 77°F, you would calculate the velocity as follows: v = 1130 + 1.1(77 - 68) v = 1130 + 1.1(9) v = 1130 + 9.9 v = 1139.9 ft/s
v = 344 + 0.6(T - 20), where v is in m/s and T is in °C
This formula is used when the temperature is measured in degrees Celsius (°C). Here's what each part means:
344 is the velocity of sound in air at 20°C (68°F) in m/s.
0.6 is the increase in velocity (in m/s) for each degree Celsius above 20°C.
(T - 20) calculates how many degrees above or below 20°C the temperature is.
So, if the temperature is 25°C, you would calculate the velocity as follows: v = 344 + 0.6(25 - 20) v = 344 + 0.6(5) v = 344 + 3 v = 347 m/s
