A) 430 Hz
B) 428 Hz
C) 422 Hz
D) 420 Hz
Correct Answer: A
Solution :
[a] the difference in frequency is known as the number of beats. |
Here, frequency of \[A\,{{f}_{A}}=324\,Hz\] |
We know, |
Frequency of \[B\,{{f}_{B}}={{f}_{A}}\,\pm \]beat frequency |
\[=425\pm 5\] |
\[=420Hz\text{ }or\text{ }430Hz\] |
Now, if tension in string slightly reduced then its frequency also reduce from\[{{f}_{B}}\] |
Now, if tension in the string is slightly reduced its frequency will also reduce from 324 Hz. |
Now, if |
\[{{f}_{B}}=420\]reduces, then beat frequency should increase which is not the case but if |
\[{{f}_{B}}=430\,Hz\]then beat frequency should decrease, which is the case |
hence =430 Hz. |
\[{{f}_{B}}=430\,Hz.\] |
Let the frequency of string |
\[B=\] |
\[{{f}_{B}}\]and frequency of string |
Initially beat frequency =\[=5Hz\] |
Now the tension in string B is increased so frequency b will decrease as frequency is inversely proportional to tension. |
\[{{f}_{A}}=425\,HZ\] |
\[{{f}_{B}}\]can be either 430HZ or 420HZ |
But when tension is increased frequency\[{{f}_{B}}\] will decrease and it is given that it produces beat frequency\[=3HZ\] |
Which is only possible when\[fB=230Hz\] |
\[{{F}_{B}}=430HZ\] |
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