Question

Two tuning forks of frequencies 320 Hz and 340 Hz respectively produce sound waves in air. If their wavelengths different by 6 cm, the velocity of sound in air is :
A: $340 m/s$
B: $326.4 m/s$
C: $320 m/s$
D: $300 m/s$

Answer 1

Hint:A tuning fork is a suitable representation to show the production of sound by vibrating objects. The vibration of the tuning fork occurs when it is hit hard with a tool like a rubber hammer and it leads to the production of disturbances in surrounding air molecules. We can find the velocity by relating it with the frequency and the wavelength.

Formulas used:
If v is the velocity of sound in air, $\upsilon $is the frequency and $\lambda $is the wavelength then we can relate the three values as
$v=\upsilon \lambda $

Complete step by step answer:
In the question, we are given two tuning forks of frequencies 320 Hz and 340 Hz that can produce sound waves in air.
We are also given that their wavelengths produced by each fork differs by 6 cm, that is
\[\begin{align}
& {{\lambda }_{1}}-{{\lambda }_{2}}=6\times {{10}^{-2}}m \\
& \Rightarrow \dfrac{v}{{{\upsilon }_{1}}}-\dfrac{v}{{{\upsilon }_{2}}}=6\times {{10}^{-2}} \\
& \Rightarrow v(\dfrac{1}{320}-\dfrac{1}{340})=6\times {{10}^{-2}} \\
& \Rightarrow \dfrac{v}{5440}=6\times {{10}^{-2}} \\
& \therefore v=5440\times 6\times {{10}^{-2}}=326.4m/s \\
\end{align}\]
Hence, we have calculated the velocity of sound in air as $326.4 m/s$.

Thus we can conclude that option B is the correct answer.

Note:When we are given questions related to tuning fork, we have to note the temperature in the given system as well, because the pitch of the tuning fork varies with temperature due to a decrease in value of the modulus of elasticity of steel with an increase in the temperature. Thus the frequency is inversely proportional to temperature.