A tuning fork vibrates with a frequency of 220 hertz

Asked by admin @ 02/08/2021 in Physics viewed by 290 People

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℃

Answered by admin @ 02/08/2021

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 $= \lambda - \lambda_0$

$=1.57-1.50=0.07m$

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