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Fleet
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Homework Statement
A certain music instrument consists of a stick of wood placed horizontally and a resonance "tube" (see attached picture, which is from the original assignment-paper) placed vertically under the stick of wood. When the wood-stick is hit, is creates a standing wave, which is amplified in the resonance "tube". The resonance "tube" is half-open (closed in botton, open in top). The music instrument is seen below:
I have to calculate the velocity of the transverse wave v_stick in the wood stick.
Information I am given:
Velocity of sound: v_sound=343 m/s
The resonance tube is four times as long as the stick of wood (the distance between the triangles on the picture)
Homework Equations
For a string with a standing wave we have that:
[itex]L=n*\frac{\lambda}{2}[/itex]
For a half-open resonance "tube" we have that:
[itex]L=(2n-1)\frac{\lambda}{4}[/itex]
L is the length of the string (wood stick) or the air "pillar" in which the standing wave exists, n is the number of the partial-tone and lambda is the wave length.
The Attempt at a Solution
[itex]4L_{stick}=L_{tube}[/itex]
I'm unsure of what i know of the wave in the resonance tube, but if I can say that the standing wave in the wood stick has n=1 and the one in the resonance tube has n=8 (see the attached picture), I get:
[itex]4\frac{lambda_{stick}}{2}=\frac{15\lambda_{tube}}{4} \Leftrightarrow 2\lambda_{stick}=\frac{15}{4}\lambda_{tube}[/itex]
I know I can insert the wave eqaution v=lambda*frequency, but what I have just seems so wrong and I have thought very long time about it. I hope you are willing to help me. I'm so stuck.
Best regards.
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