## Question

Two sitar strings *A* and *B* are slightly out of tune and produce beats of frequency 6 Hz. When the tension in string *A* is slightly decreased, the beat frequency is found to be reduced to 3 Hz. If the original frequency of *A* is 324 Hz, what is the frequency of *B*?

### Solution

318 Hz

The frequency of string *B* is

Now, the frequency of a string is proportional to the square root of tension. Hence, if the tension in A is slightly decreased, its frequency will be slightly reduced, i.e. it will become less that 324 Hz. If the frequency of string *B* is 330 Hz, the beat frequency would increase to a value greater than 6 Hz if the tension in *A* is reduced. But the beat frequency is found to decrease to 3 Hz. Hence, frequency of *B* cannot be 330 Hz; it is, therefore 318 *Hz*. When the tension in *A* is reduced, its frequency becomes 324 – 3 = 321 Hz which will produce beats of frequency 3 Hz with string *B* of frequency 318 Hz.

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