Question:
Two waves $ y=0.25\text{ }sin\,316t $ and $ y=0.25\,\sin 310\,t $ are travelling in same direction. The number of beats produced per second will be :
Two waves $ y=0.25\text{ }sin\,316t $ and $ y=0.25\,\sin 310\,t $ are travelling in same direction. The number of beats produced per second will be :
Updated On: Apr 22, 2023
- 3
- 6
- $ 3\pi $
- $ 3/\pi $
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The Correct Option is D
Solution and Explanation
Comparing the given equations with the standard equation of wave. We have $ {{n}_{1}}=\frac{316}{2\pi } $ and $ {{n}_{2}}=\frac{310}{2\pi } $ hence number of beats is $ =\frac{316}{2\pi }-\frac{310}{2\pi }=\frac{6}{2\pi }=\frac{3}{\pi } $
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Concepts Used:
Beats
What is Beat Frequency?
Let’s see from fig.m, the frequency of a pink-colored wave is f1, and that of a green-colored wave is f2. So, the frequency of the beat is the difference between these two, which is:
fBEATS = |f1 - f2|
Interference and Beats
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
What is Interference?
When two or more waves travelling in a medium meet, the resulting phenomenon is called interference and beats are an excellent example of the phenomenon of interference.
The Application of Beats:
- Beats are used in determining the unknown frequency
- Beats are used in determining the existence of poisonous gases in mines.