A) 430 Hz
B) 428 Hz
C) 422 Hz
D) 420 Hz
Correct Answer: A
Solution :
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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