A 0.70 m wooden bar is made into a marimba key, which vibrates when struck with

Question

A 0.70 m wooden bar is made into a marimba key, which vibrates when struck

with a mallet. A pin is located in the exact center of the bar, forcing a vibrational

node there. The two ends are free, and so are vibrational antinodes.

(a) Draw the standing wave patterns for the two lowest vibrational standing waves

for this system.

(b) If the lowest frequency mode is 262 Hz, what is the speed of the vibrational wave

in the wood?

(c) Find the frequency of the next lowest mode.

PLEASE SHOW ALL WORK! I need to know how to do this!

Explanation / Answer

a)

b) fundamental frequency, f = v/(2*L)

v = f*2*L = 262*2*0.7 = 366.8 m/s

c) next lowest frquency = 2*f = 524 Hz

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