Vibrations and Waves Legacy Problem #7 Guided Solution
Problem*
A geological disturbance in California produces seismic waves which are detected in Phoenix, approximately 990 km from the epicenter. If the waves travel 6.3 km/s, determine the time delay between the disturbance and the detection.
Audio Guided Solution
The speed of a wave is the distance it travels per unit of time. In equation form, that would be v, for speed, is equal to d, for distance, divided by t, for time. v equals d over t. In this problem, what I have is the speed at which seismic waves are traveling, 6.3 km per second, and the distance it travels, 990 km. What I wish to calculate is the time it takes for the wave to travel this 990 km, at this v of 6.3 km per second, from the location of the quake to a detector in Phoenix. So, given that I know d and v, and I wish to calculate t, I have to use this equation, v equals d over t, but use it to solve for t. So, if I multiply both sides of the equation by t, it becomes v times t equals t, and then if I divide through by v, that gives me t by itself, and t would be equal to d divided by v. So, I take my d of 990 km and divide it by the v of 6.3 km per second. The kilometers would cancel, and the units on your answer would be in seconds. The number comes out to be about 157.14 or so, and that's in units of seconds, and I can round this to two significant digits, such that it becomes 160 seconds.
Solution
160 seconds (rounded from 157 seconds)
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = 12.8 \unit{\meter\per\second}\), \(\descriptive{λ}{λ,wave length} = 4.52 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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