Question

The air in a closed tube 34 cm long is vibrating with two nodes and two antinodes and temperature is ${51}^{\circ }C$. What is the wavelength of the waves produced in air outside the tube, when the temperature of air is ${16}^{\circ }C$ ?

• A. 42.8 cm
• B. 68 cm
• C. 17 cm
• D. 102 cm

Answer 1

Answer: (A)

42.8 cm

Let the wavelengths of the waves at ${51}^{o}C$ and ${16}^{o}C$ be $\lambda$ and ${\lambda }^{\prime }.$

Given: Length of the pipe $L=34cm$

Thus $\frac{3\lambda }{4}=L=34cm⟹\lambda =45.33cm$

Now $T={51}^{o}C=324K$ and $T^{\prime }={16}^{o}C=289K$

As $v=\nu \lambda ⟹v\propto \lambda$ (as frequency remains the same when temperature varies)

Thus $\frac{{\lambda }^{\prime }}{\lambda }=\frac{v^{\prime }}{v}=\sqrt{\frac{T^{\prime }}{T}}$

$\frac{{\lambda }^{\prime }}{45.33}=\sqrt{\frac{289}{324}}$

$⟹{\lambda }^{\prime }=42.8cm$