Question

A vertical tube one meter long is open at the top. It is filled with 50 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?

Answer 1

The fundamental resonance frequency is 172 Hz.

Step-by-step explanation:

Given;

velocity of sound, v = 344 m/s

total length of tube, Lt = 1 m = 100 cm

height of water, hw = 50 cm

length of air column, L = Lt - hw = 100 cm - 50 cm = 50 cm

For a tube open at the top (closed pipe), the fundamental wavelength is given as;

Node to anti-node (N ---- A) : L = λ / 4

λ = 4L

λ = 4 (50 cm)

λ = 200 cm = 2 m

The fundamental resonance frequency is given by;

`f_0 = (v)/(\lambda)\\\\f_0 = (344)/(2)\\\\f_0 = 172 \ Hz\\\\`

Therefore, the fundamental resonance frequency is 172 Hz.