You are helping a friend design a new outdoor sculpture for the holiday season.

Question

You are helping a friend design a new outdoor sculpture for the holiday season. It consists of a 5-meter long cord that is stretched taut, horizontally between two attachments points. Two small, lightweight LED lights are fastened on the string, 2 meters from opposite attachment points. Someone viewing the sculpture can pull a lever that causes a sinusoidal wave to be generated at one end of the string and propogate down the string. The LED's have internal acceleration sensors that trigger the light to flash if the acceleration reaches 200 m/s^2. Your friend asks you what frequency and amplitude the wave generator should produce so that the LED's flash in unison. You start by measuring the speed of waves on the cord, 6 m/s.

Explanation / Answer

so a = A w^2

we want them to be shifted by a wavelength

so wavelength = 1 m

so f = v/wavelength = 6 Hz

200 = A *(2*pi*6)^2

A =0.14 m

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