Gravitational Wave Strain Magnitude

Classical Mechanics Level 1

The radius of a proton is about $10^{-15}$ meters. If a $4 \text{ km}$ arm of the Advanced LIGO apparatus is displaced by just the radius of a proton, what strain does this correspond to? (What does this say about the detectability of gravitational waves?)

1 \times 10^{-26}

2.5 \times 10^{-19}

2.5 \times 10^{-16}

4 \times 10^{-5}

1 solution

Matt DeCross
Feb 12, 2016

The strain of a gravitational wave is: $h= \frac{\Delta L}{L}.$ Here $L$ is the arm length and $\Delta L$ is the displacement of that arm by a proton radius. Plugging in numbers gets the answer directly.

This says detecting gravitational waves is extremely hard!

Gravitational Wave Strain Magnitude

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