Answer to Question #123103 in Physics for Katie

Question

In an experiment, a glass tube is submerged into a larger graduated cylinder full of water. A tuning fork is vibrating above the tube at a frequency of 659 Hz. If the 1st resonant frequency is heard at 14.2 cm, what is the speed of sound? Round your answer to the nearest meter.

Answer 1

The resonant frequency $f$ , the lenght of the tube $L$ and the speed of the sound $v$ are connected with the following expression (see https://en.wikipedia.org/wiki/Acoustic_resonance#Open_at_both_ends):

$$f = \dfrac{nv}{2L}$$

Expressing $v$ from this equation and setting $n=1$ (for the 1st resonant frequency), obtain:

$$v = 2fL$$

Substituting numerical values, get:

$$v = 2\cdot 659Hz\cdot 0.142m = 187.156 m/s\approx187m/s$$

Answer. v = 187 m/s.