Question

When two sound waves travel in the same direction in a medium the displacements of a particle located at 'x' at the time 't' is given by
\[{y_1} = 0.05\cos (0.50\pi x - 100\pi t)\]
\[{y_2} = 0.05\cos (0.46\pi x - 92\pi t)\] where \[{y_1},{y_2}\]and x are the meters and t in seconds. Find the speed of sound in the medium.

A. \[92m/s\]
B. \[200m/s\]
C. \[100m/s\]
D. \[332m/s\]

Answer 1

Hint: Speed of a wave is the distance at which a wave travels in a given amount of time, that is the number of meters it travels per second. It is related to the angular wave number and the frequency of a wave. The angular frequency is a vector quantity.




Formula used:
To find the speed of the wave the formula is,
\[V = \dfrac{\omega }{k}\]
Where,
\[\omega \] is angular frequency of the wave
k is angular wave number





Complete answer:
Consider a wave which is travelling in the same direction in a medium that is located at point x at a given time t. We need to find the speed of the sound at which it travels in a medium.
In order to find the speed of the wave we have,
\[V = \dfrac{\omega }{k}\]
By data, we have angular frequency as \[100\pi \] and an angular wave number is \[0.50\pi \]
Substitute the value in the above equation, we get,

\[V = \dfrac{{100\pi }}{{0.50\pi }}\]
\[V = 200m/s\]
Therefore, the speed of sound in the medium is \[200m/s\]

Hence, Option B is the correct answer



Note: Here, while solving this problem, it is important to know the formula for the speed of the wave. Don’t get confused with the formula, this is the formula to find the speed of the wave in terms of angular frequency.