Question

A person hums into the top of a well and finds that standing waves are established at frequencies of 140, 196, and 252 Hz. The frequency of 140 Hz is not necessarily the fundamental frequency. The speed of sound is 343 m/s. How deep is the well?

Answer 1

Answer:

Depth of well 3.06m

Explanation:

We know that for a pipe closed at one end the frequencies are in ratios if 1:2:3:5:7.... to the fundamental frequency

In our case the given frequencies are in the ratio of

a)$\frac{140}{196}=\frac{5}{7}$

b) $\frac{196}{252}=\frac{7}{9}$

Thus the fundamental frequency can be calculated as $140Hz=5n$

$\therefore n=\frac{140}{5}=28Hz$

Now we know that

$\lambda_{1}=4l\\\\\frac{v}{f}=4l\\\\l=\frac{v}{4f}$

Applying values we get

$L=3.06m$