assume the speed of sound in air is 360 m/s. A Quincke tube is a way to produce

Question

assume the speed of sound in air is 360 m/s.
A Quincke tube is a way to produce total destructive interference with sound by splitting the sound (of the same frequency) and then recombining it. Suppose the shorter tube is length 1.66 m.
- If the speaker produces a sound of frequency 313 Hz, what is the minimum length of the longer tube for which you get total destructive interference?
length = (I got this one right)
- If the frequency produced by the speaker is increasing at a steady rate of df/dt = 80.9 Hz/second. To keep the total destructive interference, How fast must the longer tube be increasing in length when the frequency is 680 Hz?
NOTE: You must give the correct sign: positive if L is increasing, negative if L is decreasing.
dL/dt = cm/s (This is the one I need help with!)

Explanation / Answer

A) let the lenth of the longer tube =L

so 2(L-1.66)=Lambda/2=v/2*f=343/2*313

==> L=2.203 m

B) differentiating the first eqn

==> 2*dL/dt=(v/2)*(-1/f^2)*df/dt

here df/dt=80.9

f=680

v=343

putting these values

dL/dt=-1.8544 E-4 m/s=-0.0185 cm/s

here minus sigh denotes that the length is to be decreased

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