Question

Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be

• A. 186 Hz
• B. 225 Hz
• C. 256 Hz
• D. 280 Hz

Answer 1

The correct option is A 186 Hz

We know that, for a string, frequency is proportional to square root of Tension in the string.

i.e., $f\propto \sqrt{T}$

Let the tuning fork frequency be $f$ and frequency of the string be $f_1$ and $f_2$ for the values of tension as $225N$ and $256N$ respectively.

Thus, $\frac{f_1}{f_2}=\sqrt{\frac{225}{256}}=\frac{15}{16}$

As the tuning fork produces $6$ beats per second on each of the case, we have $f-f_1=6$ and $f_2-f=6$

Using $16f_1=15f_2$, we have $15(f_2-f)+16(f-f_1)=(16+15)\times 6$

$\Rightarrow f=31\times 6=186Hz$