Asked Oct 31, 2019
A Helmholtz resonator is observed to oscillate at 400 Hz when someone blows across the top of it. If it is filled halfway up with water and then air is blown across it, what frequency would it resonate at?

Expert Answer

Step 1

The formula for the frequency of Resonance is:

Step 2

The resonator is same only the volume of the cavity is changed. Therefore, the relation between the new frequency and original frequency is:


Image Transcriptionclose

A 1 27(V) Leg (fH)NES (f#)original new new A 27 (V original e (Vo)original (f#)NC new 1 (v), |(Sx)orginal (V) new

Step 3

Now, it is filled halfway with water. Theref...


Image Transcriptionclose

(SH 400 Hz 2 (S#) (400 Hz) new =565.7 Hz


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