Measuring the wave speed
Wave calculations
Speed can be calculated using the formula:
\(Speed=\frac{distance}{time}\)
\(v=\frac{d}{t}\)
Speed\((v)\) is in metres per second \(m\,s^{-1}\), distance \((d)\) in metres \((m)\) and time\( (t)\) in seconds \((s)\).
Distance can be measured with a metre stick, Measuring device for distances ranging from a few metres to a few hundred metres., measuring tape or any other suitable device.
Example
Measuring the speed of sound waves:
Measuring the time taken for a sound wave to move from one point to another is difficult. Within a laboratory, or room, and when someone talks to you it seems that there is no time difference between making a sound and hearing it.
There is a very small time difference but we cannot measure it using a stopwatch – human reaction time would interfere with the measurement. Instead a computer, or electronic timer, must be used to measure the time.
The computer must listen for the sound wave using two microphones or sound switches. The timing process is started and then stopped when the sound reaches each microphone in turn.
\(Speed\,of\,sound = \frac{{measured\,distance}}{{time\,on\,computer}}\)
If the distance between the microphones is \(3\cdot 4\,\,m\) and the time taken for the sound wave travel is \(0\cdot 01s\), then the speed of sound can be calculated.
\(d=3\cdot 4\,\,m\)
\(t = 0\cdot01s\)
\(v = ?\)
\(v=\frac{d}{t}\)
\(v=\frac{3.4}{0.01}\)
\(v = 340\)
The speed of sound calculated is \(340 m\,s^{-1}\).
As long as you know the distance and the time, the speed of sound can be calculated. Since the speed of sound in air is a constant, if we know how long it takes for a sound to travel, we can calculate the distance it travels.
Example
Question
In a thunderstorm, there is a flash of lightning and a student hears the thunder 5 seconds later.
How far away is the thunderstorm?
(In this example, the speed of light is \(3\times 10^{8} m\,s^{-1}\) and so travels almost instantaneously compared to the sound).
\(v=\frac{d}{t}\)
\(d = ?\)
\(v=340\,m\,s^{-1}\)
\(t = 5s\)
\(340=\frac{d}{5}\)
\(d = 340 \times 5\)
\(d = 1700m\)
The thunderstorm is \(1700m\) away.
This type of calculation can be used in any type of wave: sound in a liquid or solid or even light waves.
