Question

Five beats per second are produced on vibrating two closed organ pipes simultaneously. If the ratio of their lengths is 21/20, then their frequencies will be

• A. 105 Hz and 100 Hz
• B. 105 Hz and 110 Hz
• C. 100 Hz and 105 Hz
• D. 110 Hz and 105 Hz

Answer 1

The correct option is C 100 Hz and 105 Hz

$\delta \propto \frac{1}{l}$

So, $\frac{{\delta }_1}{{\delta }_2}=\frac{l_2}{l_1}=\frac{20}{21}$

${\delta }_1=\frac{20}{21}{\delta }_2$

$Beat={\delta }_2-{\delta }_1$

$5={\delta }_2-\frac{20}{21}{\delta }_2$

$5=\frac{{\delta }_2}{21}$

${\delta }_1=105Hz$

${\delta }_1=\frac{20}{21}{\delta }_2$$=\frac{20}{21}\times 105$$=100Hz$

So, ${\delta }_{1}is100Hz$ and ${\delta }_{2}is105Hz$