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

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

Tardigrade Admin · Accepted Answer

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

f \propto 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

225 N

and

256 N

respectively.
Thus,

\frac{f _{1}}{f _{2}} = \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

16 f_{1} = 15 f_{2}

,
we have

15 (f_{2} - f) + 16 (f - f_{1}) = (16 + 15) \times 6

\Rightarrow f = 31 \times 6 = 186 Hz

Q. 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

$186 Hz$

$225 Hz$

$256 Hz$

$280 Hz$

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

186Hz

225Hz

256Hz

280Hz

Q. 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

$186 Hz$

$225 Hz$

$256 Hz$

$280 Hz$