Question

16 tuning forks are arranged in the order of increasing frequencies. Any two successive fork give 8 beats per sec when sounded together. If the last fork gives the octave of the first, then the frequency of the first fork is-

• A. n = 120
• B. n = 160
• C. n = 180
• D. n = 220

Answer 1

The correct option is A n = 120

Let the frequency of the first forks be $n$. Then the frequencies of the successive forks will be $(n+8),(n+16)........+2n$. This forms an arithmetic progression. The last term $L$ is $2n$ the first term $A$ is $n$ and the common differenceis $8$

Since,

$L=A+(N-1)d$

$2n=n+(16-1)8$

$n=120$