contestada

A child’s train whistle replicates a classic conductor’s whistle from the early 1900s. This whistle has two open-open tubes that produce two different frequencies. When you hear these two different frequencies simultaneously, you may have the perception of also hearing a lower note, called a difference tone, that is at the same frequency as the beat frequency between the two notes. The two tubes of the whistle are 12 cm and 11 cm in length. Assuming a sound speed of 350 m/s, what is the frequency of this difference tone?

Respuesta :

Answer: f2 - f1 = 132.52Hz.

Explanation: Since both tube are open at both ends, the length of air in the tube ( distance between antinode and antinode) is related to wavelength with the formulae below.

L = λ/2

considering the first tube, L1 = 12cm= 0.12m

λ1 = L1/2 = 0.12*2

λ1 = 0.24m

But v = f1 * λ1

350 = f1 * 0.24

f1 = 350/ 0.24

f1 = 1458.33Hz

Considering the second tube L2 = 11cm = 0.11m

L2 = λ2/2 = λ2 = 2* L2

λ2 = 2 * 0.11

λ2 = 0.22m

But v = fλ

350 = f2 * 0.22

f2 = 350/0.22

f2 = 1590.91

Frequency difference = f2 - f1 = 1590.91 - 1458.33

f2 - f1 = 132.52Hz