(20 pts) A 0.500 m metal bar is made into a glockenspiel key, which vibrates whe

Question

(20 pts) A 0.500 m metal bar is made into a glockenspiel key, which vibrates when struck with a mallet. Two pins are equal distances d from each end of the bar, and cause vibrational nodes there. The ends of the bar are free, and so are vibrational antinodes.

(a) Where are the pins located so that the fundamental (lowest frequency) resonant mode has the longest possible wavelength?

(b) If the fundamental mode has a frequency of 2093 Hz, what is the speed of the vibrational wave in the metal?

The answer for part a should be d=0.125 m from each end of the bar and for part b should be 1047m/s. I am just not sure how to find it.

Explanation / Answer

><.............pin....................pin.............><

   d      0.5-d             d

   L/4      L/2              L/4

lenght of the bar l = lambda/4 + lambda/2 + lambda/4 = 0.5

wavelength lambda = 0.5 m

but d = lambda/4

d = 0.5/4 = 0.125 m

===================

speed v = lambda*f

v = 0.5*2093 = 1047 m/s

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