Question

Two tuning forks when sounded together produce 6 beats per second. The first fork has the frequency $3\text{\%}$ higher than a standard one and the second has the frequency $2\text{\%}$ less than the standard fork. The frequencies (in Hz) of the forks are :

• A. $126.3,116.7$
• B. $162.3,161.7$
• C. $136.2,137.2$
• D. $123.6,117.6$

Answer 1

The correct option is D $123.6,117.6$

Gioven, ${\nu }_1={\nu }_0+\frac{3{\nu }_0}{100}={\nu }_0(1+\frac{3}{100})$ .......Eq. 1

${\nu }_0$ is the standard frequency

${\nu }_2={\nu }_0-\frac{2{\nu }_0}{100}={\nu }_0(1-\frac{2}{100})$ .......Eq. 2

Dividing Eq. 2 by Eq. 1

$\frac{{\nu }_2}{{\nu }_1}=\frac{0.98}{1.03}$

$1-\frac{{\nu }_2}{{\nu }_1}=1-\frac{0.98}{1.03}$

Using ${\nu }_1-{\nu }_2=6$ we get ${\nu }_1=123.6\text{and}{\nu }_2=117.6$