On a marimba, the wooden bar that sounds a tone when struck vibrates in a transv

Question

On a marimba, the wooden bar that sounds a tone when struck vibrates in a transverse standing wave having three antinodes and two nodes. The lowest frequency note is 87 Hz, produced by a bar 37.0 cm long. (a) Find the speed of transverse waves on the bar. (Please provide numerical answers in m/s) (b) A resonant pipe suspended vertically below the center of the bar enhances the loudness of the emitted sound. If the pipe is open at the top end only and the speed of sound in air is 350 m/s, what is the length of the pipe required to resonate with the bar in part (a)? (Please provide numerical answers in meters)

Explanation / Answer

v = f

= ( 87.0 Hz )( 0.37 m )

= 32.19 m/s

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For the fundamental standing wave in a tube open at one end,

= 4 L

so that L = / 4 = v /4f

= 350 / (4 * 87)

= 1.005 m

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