Answer:
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, ...
