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1) The fundamental frequency of a pipe that is open at both ends is 611 Hz. (Let the speed of sound be 344 m/s.) (a) How long is this pipe? (b) If one end is now closed, find the wavelength of the new fundamental. (c) If one end is now closed, find the frequency of the new fundamental. 2) A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.390 m long and has a mass of 3.00 g. (a) What is the frequency of its fundamental mode of vibration? (b) What is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 14,000 Hz? 3) Sound having frequencies above the range of human hearing (about 20,000 Hz) is called ultrasound. Waves above this frequency can be used to penetrate the body and to produce images by reflecting from surfaces. In a typical ultrasound scan, the waves travel through body tissue with a speed of 1500 m/s. For a particular scan, the wavelength should be no more than 0.913 mm. What frequency sound is required for a good scan? 4) One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at 120 Hz. The other end passes over a pulley and supports a 1.60 kg mass. The linear mass density of the rope is 0.0530 kg/m. (a) What is the speed of a transverse wave on the rope? (b) What is the wavelength? (c) How would your answers to parts (a) and (b) be changed if the mass were increased to 3.10 kg?
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