Question

There are $26$ tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives $3$ beats with the next. The first one is octave of the last. What is the frequency of $18th$ tuning fork?

• A. 100 Hz
• B. 99 Hz
• C. 96 Hz
• D. 103 Hz

Answer 1

Answer: (B)

99 Hz

Answer 2

Frequencies of 26 tuning forks will be in arithmetic progression. Frequency of two consecutive forks is 3. $\therefore$ $f={{f}_{1}}+(n-1)$ (arithmetic progression) Given, ${{f}_{1}}=2f,n=26,d=-3$ $f=2f+(26-1)(-3)$ $f=75\,Hz$ Frequency of 18th tuning fork is ${{f}_{18}}={{f}_{1}}+(18-1)(-3)$ ${{f}_{18}}=2\times 75++17\times (-3)$ ${{f}_{18}}=150-51=99\,Hz$