Question

Two open pipes, whose lengths are $50cm$ and $51cm$ respectively, produce five beat per second when sounded together. The fundamental frequencies in Hertz will be

• A. $65and60$
• B. $90and95$
• C. $95and90$
• D. $255and250$

Answer 1

The correct option is D $255and250$

For open pipe fundamental frequency ${\nu }_0=\frac{v}{2l}$, where v is the velocity of sound and l is the length of the pipe.
$\frac{{\nu }_{01}}{{\nu }_{02}}=\frac{l_2}{l_1}$
$1-\frac{{\nu }_{01}}{{\nu }_{02}}=1-\frac{l_2}{l_1}$
$\frac{{\nu }_{02}-{\nu }_{01}}{{\nu }_{02}}=1-\frac{50}{51}$
Using ${\nu }_{02}-{\nu }_{01}=5$

${\nu }_{02}=255$ and ${\nu }_{01}=250$
Ans:D