Question

A tuning fork vibrates with a frequency of 220 hertz and wavelength 1.5 m at stp. What will be increase in wavelength when temperature of air is 27℃

Answer 1

Given:

• $f=220Hz$

• $\lambda_0 =1 .5m$

• $T_0 = 0^\circ C = 273K$

To Find:

• What will be increase in wavelength when temperature of air is $27^\circ C$

Solution:

      $v_0 = f \lambda_0$

          $=220 \times1.5$

     $v_0 =330m/s$

Final temperature,$T = 273 + 27 = 300 K$

Let $v$ the speed of sound at this temperature

          $\frac{v}{v_0} = \sqrt{\frac{T}{T_0} }$

           $v = v_0 \times \sqrt{\frac{T}{T_0} }$

          $v = 330 \times \sqrt{\frac{300}{273} }$

          $v = 346.1 m/s$

Final wavelength

          $\lambda = \frac{v}{f}$

          $\lambda = \frac{346.1}{220}$

         $\lambda =1.57m$

Increase in wavelength $= \lambda - \lambda_0$

                                         $=1.57-1.50=0.07m$