Question:
Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency still remains unchanged. Denoting by $T_{1}$ and $T_{2},$ the higher and the lower initial tensions in the strings, it could be said that while making the above changes in tension:
Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency still remains unchanged. Denoting by $T_{1}$ and $T_{2},$ the higher and the lower initial tensions in the strings, it could be said that while making the above changes in tension:
Updated On: Aug 1, 2022
- $T_{1}$ was decreased
- $T_{1}$ was increased
- $T_{2}$ was increased
- $T_{2}$ was decreased
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The Correct Option is A
Solution and Explanation
The relation for frequency and tension is given by
$f \propto \sqrt{T}$
As $T_{1}>T_{2}$ i.e., $f_{1}>f_{2}$
So, $f_{1}-f_{2}=6\, Hz$
when we increase lower tension $T_{2}$,
then $f_{2}$ will be increased and $f_{1}$
will decrease Hence, $f_{2}-f_{1}=6\, Hz$
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Notes on beats
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.