Question

Two sound notes have wavelengths $\frac{83}{170}$m and $\frac{83}{172}$m in the air. These notes when sounded together produce $8$ beats per second. Calculate the velocity of sound in the air and frequencies of the two notes.

Answer 1

Given : ${\lambda }_1=\frac{83}{170}$ m and ${\lambda }_2=\frac{83}{172}$ m

Beat frequency $b=|{\nu }_2-{\nu }_1|$

Or $b=v|\frac{1}{{\lambda }_2}-\frac{1}{{\lambda }_1}|$

where $v$ is the velocity of sound in air.

Or $8=v|\frac{172}{83}-\frac{170}{83}|$

Or $8=\frac{2v}{83}$

$⟹$ $v=332m/s$