Answer to Question #219381 in Physics for yourmom

Question

The speed of sound is 340 m/s where a tuning fork produces the second resonance position above a closed air column that is 49.8 cm in length. The frequency of the tuning fork is ___ Hz. (Give your answer with the correct number of sig digs and do not include units in your answer)

Answer 1

The second resonance position corresponds to the third harmonic of the closed air column. Therefore, we can find the wavelength of the wave:

$$\lambda=\dfrac{4}{3}L=\dfrac{4}{3}\cdot0.498\ m=0.664\ m.$$

Finally, we can find the frequency of the tuning fork:

$$v=f\lambda,$$ $$f=\dfrac{v}{\lambda}=\dfrac{340\ \dfrac{m}{s}}{0.664\ m}=510\ Hz.$$