Speed of Sound:
Sound is a mechanical wave that travels through a medium. The speed of sound tells us how fast a sound wave travels through that medium. The speed is represented by \(v\), and its SI unit is metre per second \(ms^{-1}\).
Three important quantities are related to the speed of a sound wave:
- Speed — \(v\)
- Wavelength — \(\lambda\)
- Frequency — \(\nu\)
The relationship between them is:
\(v=\lambda\nu\)
Understanding the formula \(v=\lambda\nu\)
The wavelength \(\lambda\) is the distance travelled by a wave during one complete vibration or one time period.
If the time taken for one complete vibration is \(T\), then:
\(v=\frac{\lambda}{T}\)
Frequency is the number of complete vibrations made per second. Therefore,
\(\nu =\frac{1}{T}\)
So,
\(T =\frac{1}{\nu}\)
Substituting this into the speed equation:
\(v =\frac{\lambda}{T}\)
\(v =\frac{\lambda}{1/\nu}\)
Therefore,
\(v=\lambda \nu\)
What happens when Frequency changes?
The relationship between speed, wavelength and frequency must be understood carefully.
For a particular medium and temperature, the speed of sound is fixed for the conditions being considered.
Therefore, if the frequency of a sound wave increases while the speed remains constant:
\(v=\lambda \nu\)
then the wavelength must decrease. Similarly, if the frequency decreases, the wavelength increases.
Speed of Sound depends on the medium:
Sound does not travel at the same speed through all materials.
The medium through which sound travels affects its speed. Sound can travel through solids, liquids and gases, but its speed is different in each medium.
For example, the approximate speeds of the sound in different medium are:
| Medium | Approximate speed of sound |
|---|---|
| Air | \(340\ ms^{-1}\) |
| Water | \(1500\ ms^{-1}\) |
| Steel | \(5000\ ms^{-1}\) |
Thus, under the stated conditions, sound travels fastest through steel and slowest through air.
Speed of sound also depends on Temperature:
The speed of sound in air is affected by temperature.
As the temperature of air increases, the speed of sound increases.
A time-delay problem can also be represented using a wave graph. Suppose a graph shows two corresponding points of a wave, such as two successive crests. The time difference between them gives the time period \(T\).
- At \(0^{\circ}C\): \(331\ ms^{-1}\)
- At \(15^{\circ}C\): \(340\ ms^{-1}\)
- At \(22^{\circ}C\): \(344\ ms^{-1}\)
Therefore as temperature increases, the speed of sound in air increases.
Speed, Frequency and Wavelength:
These three quantities are related, but they do not mean the same thing.
Speed (\(v\))
- \(v=speed\)
- \(d=distance\ travelled\)
- \(t=time\ taken\)
Rearranging:
\(d=vt\)
Therefore, if the speed of sound and the time taken by sound to reach an observer are known, the distance can be calculated.
Lightning and Thunder: Why Is There a Time Delay?
During a thunderstorm, lightning is seen before thunder is heard. This happens because light reaches us much faster than sound.
Therefore, although the lightning and thunder are produced almost at the same event, we see the lightning first and hear the thunder later.
The time interval between seeing the lightning and hearing the thunder can be used to estimate the distance of the thundercloud.
For this calculation, the time delay is treated as the approximate travel time of the sound.
Time Delay from a Wave Graph:
If the speed of the wave is known:
\(v=\frac{\lambda}{T}\)
Therefore:
\(\lambda =vT\)
If the graph gives the time interval in microseconds, remember:
\(1\mu s=10^{-6}s\)
So, the time must be converted into seconds before using the formula if the speed is given in \(ms^{-1}\).