Chapter 17: Q10CQ (page 628)
What is the difference between an overtone and a harmonic? Are all harmonics overtones? Are all overtones harmonics?
All resonant frequencies higher than fundamental frequency are called overtones and the fundamental frequency along with the overtones are known as harmonics.
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Calculate the first overtone in an ear canal, which resonates like a 2.40 cm long tube closed at one end, by taking air temperature to be 37.0 C. Is the ear particularly sensitive to such a frequency? (The resonances of the ear canal are complicated by its nonuniform shape, which we shall ignore.)
(a) Students in a physics lab are asked to find the length of an air column in a tube closed at one end that has a fundamental frequency of 256 Hz. They hold the tube vertically and fill it with water to the top, then lower the water while a 256 Hz tuning fork is rung and listen for the first resonance. What is the air temperature if the resonance occurs for a length of 0.336 m?
(b) At what length will they observe the second resonance (first overtone)?
A sonar echo returns to a submarine \(1.20\;{\rm{s}}\) after being emitted. What is the distance to the object creating the echo? (Assume that the submarine is in the ocean, not in fresh water.)
(a) Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce if its sound gathering area is\(900\;{\rm{c}}{{\rm{m}}^{\rm{2}}}\)and the area of the eardrum is\(0.500\;{\rm{c}}{{\rm{m}}^{\rm{2}}}\), but the trumpet only has an efficiency of\(5.00\% \)in transmitting the sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a)
(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is18.0C. (b)What is its fundamental frequency at 25.0 C?
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