MCQ
Two sound waves of wavelength ${\lambda _1}$ and ${\lambda _2}$ $\left( {{\lambda _2} > {\lambda _1}} \right)$ produce $n\, beats/s$, the speed of sound is
  • $\frac{{n{\lambda _1}{\lambda _2}}}{{{\lambda _2} - {\lambda _1}}}$
  • B
    $n\,\left( {\frac{1}{{{\lambda _1}}} - \frac{1}{{{\lambda _2}}}} \right)$
  • C
    ${n\,\left( {{\lambda _2} - {\lambda _1}} \right)}$
  • D
    ${n\,\left( {{\lambda _2} + {\lambda _1}} \right)}$

Answer

Correct option: A.
$\frac{{n{\lambda _1}{\lambda _2}}}{{{\lambda _2} - {\lambda _1}}}$
a
In same media, speed of sound will be same speed 

$\mathrm{v}=\mathrm{f}_{1} \lambda_{1}=\mathrm{f}_{2} \lambda_{2}$

now Beats $=\mathrm{f}_{1}-\mathrm{f}_{2}$

$\mathrm{n}=\frac{\mathrm{v}}{\lambda_{1}}-\frac{\mathrm{v}}{\lambda_{2}} \mathrm{v}=\frac{\mathrm{n} \lambda_{1} \lambda_{2}}{\lambda_{2}-\lambda_{1}}$

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