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    Evaluating Standing Waves

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    1. For a particular tube there are six harmonic frequencies below 1000 Hz. Four of these are 300Hz, 600Hz, 750Hz, and 900Hz. You can see that one end of the tube is open, but you can not see the other end. Is it open or closed? Explain your answer.

    2. In the tube described above, what two frequencies are missing?

    3. When a musical note is played on a large church pipe organ, the sound originates from blowing puffs of air into a tube of a fixed length. Does this puff of air have to have only the particular frequency of the final note? If so, how do you think the organ creates the puff with this frequency? If it does not, why you you think you only hear a singe frequency?

    4. The audible frequency range for normal hearing is from about 20Hz to 20 kHz. What are the wavelengths of sound waves at these frequencies?

    5. A small loudspeaker driven by an audio oscillator and amplifier, adjustable in frequency. Nearby is a tube of cylindrical sheet-metal pipe 45.7 cm long, with a diameter of 2.3 cm and which is open at both ends. If the room temperature is 20 degrees Celsius, at what frequencies will resonance occur in the pipe when the frequency emitted by the speaker is varied from 1000 to 2000 Hz.

    6. a) What is the fundamental frequency of the tube in the previous problem?
    b) What would be the fundamental frequency if we doubled the diameter of the to 4.6cm?
    c) What would be the fundamental frequency if we doubled the length of the tube to 91.4cm?
    d) What would be the fundamental frequency if we decreased the velocity of sound in air to 320 m/sec?

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    Solution Preview

    Here are answers to your problems:

    1) An organ pipe which is open at both ends can produce fundamental of frequency f and harmonics of frequencies 2f,3f, 4f etc. That is even as well as odd harmonics. An organ pipe which is open at one end and closed at the other can produce only odd harmonics. That is, f, 3f, 5f etc., if f is fundamental.The pipe in question is open at both ends and is capable of producing a fundamental frequency of 150 Hz and harmonics of 300Hz, 450Hz, 600Hz, 750Hz and 900Hz(below 1000Hz). Of these, ...

    Solution Summary

    This solution provides a detailed, step-wise response, including all of the required calculations.