A slide whistle is an open-closed tube with an adjustable plunger that changes the length. You are playing the slide whistle and pushing the plunger in at 8 cm/s when the tube is 15 cm long. What is the rate of change of the sound in Hz/s?

df / ft = - n 12 n = 1, 3, 5, ...

Explanation:

The speed of sound is

v = λ f

In a whistle that we approach by an open tube at one end and closed at the other, standing waves occur, which has a node in the closed part and a maximum in the open pate, whereby wavelength and the distance of the tube are related, the fundamental wave is

λ₁ = 4L

The harmonics are

λ₃ = 4L / 3

λ₅ = 4L / 5

The general formula

λₙ = 4L / n

with n = 1, 3, 5, ...

We substitute and clear in the first equation

f = v n / 4L n = 1, 3, 5, ...

Let's use derivatives to find the frequency change

df / dt = v n / 4 dL⁻¹ / dt

d / dt (1/L) = - 1 / L² dL / dt

Where dL / dt = 8 cm / s

We replace

df / dt = - n v / L2 dL / dt

Let's calculate

df / dt = - n 340/152 8

df / ft = - n 12 n = 1, 3, 5, ...