Question

Two tuning forks when sounded together produce $6$ beats per sec. The first fork has the frequency $3$% higher than a standard one and the second has the frequency $2$% less than the standard fork. The frequency of the forks are

• A. $126.3,120.3Hz$
• B. $162.7,156.7Hz$
• C. $136.2,130.2Hz$
• D. $123.6,117.6Hz$

Answer 1

The correct option is D $123.6,117.6Hz$

Given beat frequency$f_1-f_2=6$
let $f$ be standard frequency
$f_1=(f+\frac{3f}{100})$( $3$% higher)
$f_2=(f-\frac{2f}{100})$( $2$% lower)

$(f+\frac{3f}{100})-(f-\frac{2f}{100})=6$

$\Rightarrow 5f=600orf=120Hz$

$f+\frac{3f}{100}=123.6Hz,$

$f-\frac{2f}{100}=120-\frac{2\times 120}{100}=117.6Hz$