Question

A metal rod 0.89 m in length is held at its center. It is stroked with a rosin-coated doth to set up a longitudinal vibration. The speed of sound in a thin red of this metalls 5050 m/s (a) What is the fundamental frequency of the waves established in the rod? kHz (b) What harmonics are set up in the rod held in this manner? even odd (c) What would be the fundamental frequency if the rod were made of copper, in which the speed of sound is 3560 m/s? kHz Need Help? Rand 19. -/1 POINTS SERPSET9 18.P.056. MY NOTES ASK YOUR TEACHER While attempting to tune the note Cat 277 HZ, a plano tuner hears 5.00 beats/s between a reference oscillator and the string. (a) What are the possible frequencies of the string? (Give the frequencies to the nearest Integer.) lower possible frequency higher possible frequency (b) When she tightens the string slightly, she hears 0.00 beats. What is the frequency of the string now? (Give the frequency to the nearest Integer.) (C) By what percentage should the piano tuner now change the tension in the string to bring it into tune (Give a positive answer for an increase in the tension or a negative answer for a decrease in the tension.) 6:10 AM

Answer 1

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(a) The mode pattern is ANA, corresponding to the fundamental mode. The length of the rod is one wavelength: v 5050 2.84 kHz 1 2L (2)(0.89) Since it is held in the center, there must be a node in the center as well as antinodes at the ends. The even harmonics have an antinode at the center so only the odd harmonics are present. (b) (c) The wavelength is the same as in (a): V 3560 JE 2L (2)(0.89) = 2.00 kHz

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