When two sound waves travel in the same direction in a...

When two sound waves travel in the same direction in a medium, the displacement of a particle located at $\mathrm{x}$ at time $\mathrm{t}$ is given by $\mathrm{y}_{1}=0.05 \cos (0.50 \mathrm{px}-100 \mathrm{pt}) \&$ $\mathrm{y}_{2}=0.05 \cos (0.46 \mathrm{px}-92 \mathrm{pt})$, where $\mathrm{y}_{1}, \mathrm{y}_{2}$ and $\mathrm{x}$ are in meter and $\mathrm{t}$ is in seconds. At $\mathrm{x}=0$, how many times between $\mathrm{t}=0$ and $\mathrm{t}=1 \mathrm{~s}$ does the resultant displacement become zero ? (A) 46 (B) 50 (C) 92 (D) 100

When two sound waves travel in the same direction in a medium, the displacement of a particle located at $\mathrm{x}$ at time $\mathrm{t}$ is given by $\mathrm{y}_{1}=0.05 \cos (0.50 \mathrm{px}-100 \mathrm{pt}) \&$
$\mathrm{y}_{2}=0.05 \cos (0.46 \mathrm{px}-92 \mathrm{pt})$, where $\mathrm{y}_{1}, \mathrm{y}_{2}$ and $\mathrm{x}$ are in meter
and $\mathrm{t}$ is in seconds.
At $\mathrm{x}=0$, how many times between $\mathrm{t}=0$ and $\mathrm{t}=1 \mathrm{~s}$ does the resultant displacement become zero ?
(A) 46
(B) 50
(C) 92
(D) 100

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Superposition Principle

The superposition principle states that when two or more waves traverse the same medium, their displacements add algebraically at every point to yield the net displacement. This concept is fundamental in understanding how complex wave patterns arise from combining simpler ones.

Wave Interference

Wave interference is the phenomenon that occurs when two or more waves meet and combine. Depending on their phase relationship, the interference can be constructive (amplitudes add) or destructive (amplitudes subtract), leading to variations in the overall amplitude at different points.

Phase Difference

Phase difference refers to the relative shift between the phases of two or more wave functions. It is crucial in determining the type of interference that will occur, as specific phase differences can result in complete cancellation of the wave displacement at certain moments.

Beat Frequency

Beat frequency arises when two waves of similar but not identical frequencies interfere, resulting in periodic variations in the amplitude of the resultant wave. This phenomenon is characterized by the rate at which the amplitude goes from a maximum to zero (or vice versa), illustrating the concept of temporal interference.

Transcript

Please give Ace some feedback