Question

Two particles in a medium are vibrating in the same phase with a path difference of $10m$ and corresponding time difference is $0.1{{ sec}}$ . The speed of the wave in the medium is:
A) $100m{s^{ - 1}}$
B) $300m{s^{ - 1}}$
C) $50m{s^{ - 1}}$
D) $200m{s^{ - 1}}$

Answer 1

Phase and path difference:-
For any two waves having the same frequency, the phase and path difference are related as.
$\Delta x = \dfrac{\lambda }{{2\pi }}\Delta \phi$
Here, $\Delta x$ is the path difference between the two waves.
$\Delta \phi$ is the phase difference between the two waves.
The phase difference is the difference in the phase angle of the two waves. Path difference is the difference in the path transversed by the two waves.
The relation between the phase and path difference is direct. They are directly proportional to each other. So the path differences we have is;
$\Delta x = \dfrac{\lambda }{{2\pi }}\Delta \phi$

Complete step by step solution:
The given term here we have in the question are
Path difference = $10$ meters
Time difference = $0.1$ sec.
Here we have to calculate the speed of the wave in the given medium.
The general formula for the speed is $\dfrac{{\operatorname{Distance} }}{{\operatorname{time} }}$ .
Here the path difference $10$ meter is equivalent to the distance covered by the wave in a time period of $0.1$ sec. So the modified formula will be.
Speed $= \dfrac{{\operatorname{path} difference}}{{\operatorname{time} }}$
Speed of wave $= \dfrac{{10{{ m}}}}{{0.1\,\sec .}}$
Now after solving the above term the speed we have is.
Speed of wave $= 100m{s^{ - 1}}$
Speed $= 100m{s^{ - 1}}$

So option ‘A’ will be correct.

Additional Information: Wave: Wave involves the transport of energy without the transport of matter. In conclusion a wave can be described as a disturbance that travels through a medium, transporting energy from one location to another location without transporting matter.

The type of wave most commonly studied in classical physics are mechanical and electromagnetic. In mechanical wave stress and strain fields oscillate about a mechanical equilibrium.

Note: In an electromagnetic wave (such as light ) energy is interchanged between electronic and magnetic fields. Propagation of a wave involving these fields according to Maxwell equations. Electromagnetic waves can travel through vacuum and the same dielectric media.
Mathematical description of single wave:
A wave can be described just like a field namely as a function $F\left( {x,t} \right)$ , where $'x'$ is a position and $'t'$ is a time. The value of $'x'$ is a point space specified in the region where the wave is defined.