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*440 \\ v_(\circ)=343.2\text{ m/s} \end{gathered}`

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

`v=v_(\circ)\sqrt[]{(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*\sqrt[]{(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)=(v)/(f)`

Substituting the known values,

`\begin{gathered} \lambda^(\prime)=(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.