There are two tubes that are identical except for their slightly different lengths. Both tubes have one open end and one closed end. A speaker connected to a variable frequency generator is placed in front of the tubes. The speaker is set to produce a note of very low frequency and then turned on. The frequency is then slowly increased to produce resonances in the tubes. Students observe that at first only one of the tubes resonates at a time. Later as the frequency gets very high, there are times when both tubes resonate.
Explain why there are some high frequencies, but no low frequencies, at which both tubes resonate. Any help would be greatly appreciated :)
the tubes first resonate at their individual fundamental frequencies
... the longer tube will have a lower fundamental
the tubes will then resonate at the odd harmonics of their fundamentals
as the frequencies increase, some will be an odd multiple for both tubes
When the speaker produces a low-frequency sound, it may not be able to excite both tubes simultaneously due to their slightly different lengths. Resonance occurs when the natural frequency of an object matches the frequency of the sound waves being produced. In this case, the tubes have different lengths, so they will have different natural frequencies at which they resonate.
As the frequency of the sound waves gradually increases, it will eventually match the natural frequency of one of the tubes. At this point, that specific tube will start resonating and amplify the sound wave, resulting in a loud sound. However, the other tube, with a different length, will not resonate at this frequency, and the sound wave will not be amplified.
As the frequency continues to increase, there will come a point where the second tube's natural frequency aligns with the frequency of the sound waves produced by the speaker. At this point, both tubes will start resonating simultaneously and amplify the sound waves.
The reason there are high frequencies at which both tubes resonate, but no low frequencies, is due to the difference in the lengths of the tubes. The longer tube will have a lower natural frequency, while the shorter tube will have a higher natural frequency. Therefore, at low frequencies, only the longer tube will resonate, while at high frequencies, both tubes will resonate together.