A fork A has frequency 2% more than the standard fork and B has a frequency 3% less than the frequency of same standard fork. The forks A and B when sounded together produced 6 beats `s^(-1)` . The frequency of fork A is

Options

A. 116.4 Hz
B. 120 Hz
C. 122.4 Hz
D. 238.8 Hz

Answer

C

Explanation

Let `upsilon` be frequency of standard fork. The frequency of A, `upsilon_A=upsilon+2/100 upsilon`
the frequency of B, `upsilon_B=upsilon-3/100upsilon`
According to question ,
`upsilon_A-upsilon_B=6`
`therefore (upsilon+ 2/100upsilon)-(upsilon-3/100upsilon)=6`
`5/100 upsilon =6` or `upsilon=600/5`=120 Hz
The frequency of A
`upsilon_A=(upsilon + 2/100upsilon)=120+ 2/100 xx 120` = 122.4 Hz