Question

A tuning fork with a frequency of 440 Hz produces waves with a wavelength of 0.78 m at 20° C. What will be its wavelength at 13° C?1) 0.77 m2) 1.29 m3) 0.66 m4) 2.06 m

Answer 1

Given data:

* The frequency of the tuning fork is,

$f=440\text{ Hz}$

* The wavelength of the fork at 20 degree is,

$\lambda=0.78\text{ m}$

Solution:

The velocity of the tuning fork wave at 20 degree is,

$\begin{gathered} v_{\circ}=\lambda f \\ v_{\circ}=0.78\times440 \\ v_{\circ}=343.2\text{ m/s} \end{gathered}$

The velocity of the tuning fork wave at 13 degree is,

$v=v_{\circ}\sqrt[]{\frac{T}{T_{\circ}}}$

where,

$\begin{gathered} T=13^{\circ}C \\ T=286.15\text{ K} \end{gathered}$

and,

$\begin{gathered} T_{\circ}=20^{\circ}C \\ T_{\circ}=293.15\text{ K} \end{gathered}$

Thus, the velocity of the sound wave at 13 degree Celsius is,

$\begin{gathered} v=343.2\times\sqrt[]{\frac{286.15}{293.15}} \\ v=339.08\text{ m/s} \end{gathered}$

The wavelength of tthe sound wave at 13 degree celsius is,

$\lambda^{\prime}=\frac{v}{f}$

Substituting the known values,

$\begin{gathered} \lambda^{\prime}=\frac{339.08}{440} \\ \lambda^{\prime}=0.77\text{ m} \end{gathered}$

Thus, the wavelength of the sound wave at 13 degree celsius is 0.77 m.

Hence, option 1 is the correct answer.