[aliceingledew]

Consider a Boehm flute (the common sliver flute) that plays C4 as its lowest note and that is 597 mm long from the middle of the blowing hole to the open end of the flute. As a first approximation, model it as a 597 mm long cylindrical tube that is open at both ends. What is the fundamental resonant frequency of this tube at 20 C, neglecting end corrections?




The lowest note of the common B-flat clarinet is D3, and the total length of the instrument is about 600 mm. Model the clarinet as a cylindrical tube of this length that is closed at one end. Neglecting the end correction, what is the fundamental frequency of the tube at 20 C? Again, compare your result to the frequency for D3 given in Hall.

Suppose we need a panpipe tube with a fundamental pitch G4. (Panpipe tubes are closed at one end and open at the other.) Neglecting the end correction, and assuming an air temperature of 20 C, how long should the tube be? Express your answer in centimeters (cm).


Do the previous problem again, but this time suppose the inside diameter of the tube is 5 cm and include the effect of the end correction at the open end. The result you give should be the physical length of the tube that you would measure with a ruler (the inside length from the opening to the plug). Assume again an air temperature of 20 C, and express you answer in centimeters (cm).


Suppose we overblow the panpipe tube from the previous problem and excite the next mode above the fundamental. What is the frequency of the note we will hear? Express your answer in Hz.






Suppose the lowest note of a flute is exactly C4 at a temperature of 20 C. Now suppose the temperature rises to 25 C. How much does the frequency of the lowest note change? If the frequency goes up, give a positive result, or a negative one if it goes down. Express your answer in Hz.

[smoothy]

Consider a Boehm flute (the common sliver flute) that plays C4 as its lowest note and that is 597 mm long from the middle of the blowing hole to the open end of the flute. As a first approximation, model it as a 597 mm long cylindrical tube that is open at both ends. What is the fundamental resonant frequency of this tube at 20 C, neglecting end corrections?




The lowest note of the common B-flat clarinet is D3, and the total length of the instrument is about 600 mm. Model the clarinet as a cylindrical tube of this length that is closed at one end. Neglecting the end correction, what is the fundamental frequency of the tube at 20 C? Again, compare your result to the frequency for D3 given in Hall.

Suppose we need a panpipe tube with a fundamental pitch G4. (Panpipe tubes are closed at one end and open at the other.) Neglecting the end correction, and assuming an air temperature of 20 C, how long should the tube be? Express your answer in centimeters (cm).


Do the previous problem again, but this time suppose the inside diameter of the tube is 5 cm and include the effect of the end correction at the open end. The result you give should be the physical length of the tube that you would measure with a ruler (the inside length from the opening to the plug). Assume again an air temperature of 20 C, and express you answer in centimeters (cm).


Suppose we overblow the panpipe tube from the previous problem and excite the next mode above the fundamental. What is the frequency of the note we will hear? Express your answer in Hz.






Suppose the lowest note of a flute is exactly C4 at a temperature of 20 C. Now suppose the temperature rises to 25 C. How much does the frequency of the lowest note change? If the frequency goes up, give a positive result, or a negative one if it goes down. Express your answer in Hz.

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