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What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer

$7.00 \times 10^2 \textrm{ m}$

Solution Video

OpenStax College Physics Solution, Chapter 16, Problem 53 (Problems & Exercises) (0:47)

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Video Transcript

This is College Physics Answers with Shaun Dychko. To figure out the wave length of this earthquake we need to know the speed of the waves from the earthquake and their frequency. Now we can figure out the speed by knowing that it travels 84 kilometers in 12 seconds. Speed is distance over time and I'll write 84 kilometers as 84 times ten to the three meters, divided by 12 seconds gives us 7000 meters per second. Then we can solve for <i>lambda</i> in this formula by dividing both sides by <i>f</i>. <i>Lambda</i> is <i>v</i> over <i>f</i>. So that's 7000 meters per second divided by 10 Hertz that we're told in the question and this makes a wave length of 700 meters and I write it as 7.00 times ten to the two meters in order to indicate that these zeroes are significant.