MCQ
The speed of sound in a gas, in which two waves of wavelength $1.0\,\, m$ and $1.02\,\, m$ produce $6$ beats per second, is approximately .... $m/s$
- A$350$
- ✓$300$
- C$380$
- D$410$
✓
Answer
Correct option: B.
$300$
b
Let, $n_{1}$ and $n_{2}$ be the frequencies of two waves.
Let, $n_{1}$ and $n_{2}$ be the frequencies of two waves.
$\lambda_{1}$ and $\lambda_{2}$ be the wavelengths of two waves.
$v$ be the speed of sound.
The number of beats per second are
$n_{1}-n_{2}=6$
$\frac{v}{\lambda_{1}}-\frac{v}{\lambda_{2}}=6$
$\frac{v}{1}-\frac{v}{1.02}=6$
$\frac{0.02 v}{1.02}=6$
$0.02 v=(6)(1.02)$
$v=\frac{6.12}{0.02}=306 \mathrm{ms}^{-1} \approx 300 \mathrm{m} / \mathrm{s}$
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