Question

A 1.0 m tall vertical tube is filled with 20∘C water. A tuning fork vibrating at 578 Hz is held just over the top of the tube as the water is slowly drained from the bottom.

At what three different water heights, measured from the bottom of the tube, will there be a standing wave in the tube above the water?

Answer 1

Given data :

frequency(f) = 578 Hz

height of tube = 1 m

temperature = 20⁰ C

velocity of sound at this temp. = 343.2 m/s

Solution

We know for formation of standing wave in pipe, formula of length of tube is given by

For n = 1

We will get, L = 0.1484 m

For n = 2

We will get, L = 0.445 m

For n = 3

we will get, L = 0.742 m

So these are the lengths of tube required.

therefore, Height of water required are

h1 = 1 - 0.1484 = 0.8516 m

h2 = 1 - 0.445 = 0.555 m

h3 = 1 - 0.742 = 0.258 m