Question

Ten tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce $4$ beats per second. The highest frequency is twice that of the lowest. Possible highest and lowest frequencies (in Hz) are:

• A. $80$ and $40$
• B. $100$ and $50$
• C. $44$ and $22$
• D. $72$ and $36$

Answer 1

The correct option is D $72$ and $36$

Each fork produces 4 beats per second with the previous means each fork has frequency 4 Hz more than the previous.

So the 10th fork will have frequency $9\times 4=$36Hz more than the 1st

So this is an algebraic equation as $2x-x=36$

Hence the frequencies are 72 and 36