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You blow across the mouth of a bottle. The air column inside is 17 cm long, and sound travels at…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
You blow across the mouth of a bottle. The air column inside is long, and sound travels at . Find the lowest note the bottle gives, and the next one it can give. Why can it not give a note at twice the lowest frequency?
Need a reminder? The key ideaShow
In a pipe, a closed end is a displacement node and an open end a displacement antinode. Closed at one end: , odd harmonics only. Open at both ends: , every harmonic.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Lowest note. The bottle is a pipe closed at one end, so and .
Next note. The next mode fits three quarter wavelengths: .
Why not 1000 Hz? A note at would need half a wavelength in the bottle, with an antinode at both ends. The bottom is a node, so that pattern cannot form.
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