Solve the below given problem:
The below given graph shows the displacement versus time relation for a disturbance travelling with a velocity of \(1500\ m/s^{-1}\). Calculate the wavelength of the disturbance.
Displacement vs time graph
Given:
The displacement–time graph shows a disturbance travelling with a velocity of:
\(v=1500\ m/s^{-1}\)
We have to calculate the wavelength of the disturbance.
Step 1: Find the time period from the graph
From the graph, the first crest occurs at:
\(t_{1}=1\ \mu s\)
and the next successive crest occurs at:
\(t_{2}=3\ \mu s\)
The time period is the time interval between two successive crests.
1. What is the time period of the disturbance?
Step 2: Convert the time period into seconds
Since the velocity is given in \(ms^{-1}\), the time period should be expressed in \(seconds\).
2. What is the correct value of the time period in seconds?
Step 3: Establish the relationship and calculate wavelength
The velocity of a wave is related to its wavelength and time period by:
\(v=\frac{\lambda}{T}\)
3. Which expression should be used to calculate the wavelength of the disturbance?
Now substitute:
Therefore we get,
\(\lambda =3\times 10^{-3}\)
Step 4: Express the answer in a suitable unit
Since:
\(1\ m\ = 1000\ mm\)
4. What is the wavelength of the disturbance?