A tuning fork of frequency $220\text{ Hz}$ produces sound waves of wavelength $1.5\text{ m}$ in air at STP.…

A tuning fork of frequency $220\text{ Hz}$ produces sound waves of wavelength $1.5\text{ m}$ in air at STP. The increase in wavelength, when temperature of air is $27^\circ\text{C}$, is
  1. $0.07\text{ m}$
  2. $0.08\text{ m}$
  3. $0.09\text{ m}$
  4. $0.10\text{ m}$

Solution

Given, $\nu = 220\text{ Hz}$, $\lambda_1 = 1.5\text{ m}$, $T_1 = 0^\circ\text{C} = 273\text{ K}$ $v_1 = \nu \lambda_1 = 220 \times 1.5 = 330\text{ ms}^{-1}$ $T_2 = 27^\circ\text{C} = 27 + 273 = 300\text{ K}$ Velocity, $v_2 = v_1 \sqrt{\frac{T_2}{T_1}} = 330 \sqrt{\frac{300}{273}} = 345.9\text{ ms}^{-1}$ Wavelength, $\lambda_2 = \frac{v_2}{\nu} = \frac{345.9}{220} = 1.57\text{ m}$ Increase in wavelength $= \lambda_2 - \lambda_1 = 1.57 - 1.5 = 0.07\text{ m}$

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