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Harmonics - Section 13B


1. A 47.0 m alphorn was made in Idaho in 1989. An alphorn behaves like a pipe with one end closed. If the frequency of the fifteenth harmonic is 26.7 Hz, how long is the alphorn? The speed of sound in air is 334 m/s.


2. A fully functional acoustic guitar over 8.0 m in length is on display in Bristol, England. Suppose the speed of waves on the guitar’s strings is 5.00 x 102 m/s. If a third harmonic is generated on a string, so that the sound produced in air has a wavelength of 3.47 m, what is the length of the string? The speed of sound in air is 334 m/s.


3. The unsupported flagpole built for Canada’s Expo 86 has a height of 86 m. If a standing wave with a 19th harmonic is produced in an 86 m open pipe, what is its frequency? The speed of sound in air is 334 m/s.


4. A power-plant chimney in Spain is 3.50 x 102 m high. If a standing wave with a frequency of 35.5 Hz is generated in an open pipe with a length equal to the chimney’s height and the 75th harmonic is present, what is the speed of sound?


5. The world’s largest organ was completed in 1930 in Atlantic City, New Jersey. Its shortest pipe is 4.7 mm long. If one end of this pipe is closed, what is the number of harmonics created by an ultrasound with a wave- length of 3.76 mm?