The distance travelled by a sound wave per unit time as it propagates through an elastic medium is known as the speed of sound.
If one wavelength () represents the distance travelled by one wave, and one time period (\(T\)) represents the time taken for this propagation, then
And, we know
By applying this in speed formula, we get
Under the same physical conditions, the speed of sound in a given medium remains nearly constant for all frequencies.
Let us solve following example for better understanding.
A sound wave has a frequency of \(2\) \(kHz\) and a wavelength of \(15\) \(cm\). How much time will it take to travel \(1.5\) \(km\)?
Frequency \(=\) \(2\) \(kHz\) \(=\) \(2000\) \(Hz\)
Wavelength \(=\) \(15\) \(cm\) \(=\) \(0.15\) \(m\)
Distance \(=\) \(1.5\) \(km\) \(=\) \(1500\) \(m\)
To find: Time period
We don't know the value of speed,
Now, apply in the value of speed in time formula
The sound will take \(5\) \(s\) to travel a distance of \(1.5\) \(km\).