Answer to Question #219383 in Physics for yourmom

Question

The speed of sound where a tuning fork of frequency 262 Hz produces the third resonance position above a closed air column that is 1.59 m in length is ___m/s. (Give your answer with the correct number of sig digs and do not include units in your answer)

Answer 1

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

$$\lambda=\dfrac{4}{5}L=\dfrac{4}{5}\cdot1.59\ m=1.272\ m.$$

Finally, we can find the speed of sound:

$$v=f\lambda,$$ $$v=262\ Hz\cdot1.272\ Hz=333\ \dfrac{m}{s}.$$