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Mechanical Engineering
Dec 17, 2023
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The Science Of Acoustics Homework 6 Name: Please, show all your work clearly and and write down all your steps. Use proper units in all your answers! Please be clear! I repeat on purpose. Bottom line : No Work, no credit. No Kidding! Problem 1 - Harmonics in pipes. (30 Points) Fill in the blanks in the table below. Please show all your work below the table, and sketch each corresponding harmonic as well Type of Pipe Length of Pipe (m) Name of Harmonic Wavelength λ (m) Frequency f (Hz) Closed Pipe 0.45 Third Harmonic Open Pipe Second Harmonic 1.2 Closed Pipe 0.25 0.2 Open Pipe Third Harmonic 0.4 Closed Pipe First harmonic 3.6 Open Pipe 0.3 0.6
Problem 2 - More on standing waves in pipes. (20 Points) In this problem, assume that the speed of sound is c s = 340 m/s. A long vertical tube of Length H is completely filled with water, and it has a small tap that can be used to drop the level of water inside. A tuning fork of frequency 880 Hz is held ringing over the open end of the tube. As water flows out of the tube, the air column inside grows longer. Calculate the first three air column lengths, L 1 , L 2 and L 3 for which resonance occurs (i.e. when the sound grows loud). Draw three separate diagrams that show the standing waves in each case, and be sure to label the locations of all the nodes and the antinodes.
Problem 3 - Fundamental of a Flute (20 Points) A flute is designed to play its fundamental note at 264 Hz, when the air temperature is 15 C. Calculate the length of the flute, and the frequencies of the second and third harmonics. Please make sketches of all 3 harmonics.
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