Sound Waves Legacy Problem #5 Guided Solution
Problem*
On a recent PE-sponsored adventure education program, students went hiking at Devil's Head State Park. At one point, Jeremy let out a holler which reflected off a nearby rocky cliff and was detected as an echo 1.80 seconds later. Determine the distance to the rocky cliffs. Assume a speed of sound of 344 m/s.
Audio Guided Solution
This is a question which commonly gets missed, and not because of any mathematical difficulties, but rather because of difficulties with conceptualizing and visualizing the situation. It's a question about wave speed, the speed of a sound that travels at 344 meters per second towards the cliff and back, and it takes 1.80 seconds for that sound to travel to the cliffs and back. What we wish to calculate is the distance to the cliff. We need to use the equation that the speed of sound is the distance traveled per time. That's the definition of speed of any object, whether a sound wave, a car, or a runner. So the 344 meters per second is the distance to time ratio for these sound waves. The time for the waves to travel to the cliff and back is 1.80 seconds. Now if I rearrange the equation to solve for distance, it would become distance equal V, or speed, times the time, multiplying the 344 meters per second by the 1.80 seconds, gets me a distance value of 619.2 meters. And that's the distance the sound travels in this 1.80 seconds. But that's not the answer to the question, because the question doesn't ask what's the distance it travels in 1.80 seconds. It asks what's the distance from Jeremy to the rocky cliff. Now that's just one half of this distance, because the time we have is the time to go the two-way trip from Jeremy to cliff and back. So if I half this distance of 619.2, I get 309.6 meters. That's just the distance one way to the cliff. I can round that to two significant digits, such that it becomes 310 meters.
Solution
310 m
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., \(\descriptive{v}{v,velocity} = 345\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 1.28 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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.
Read About It!
Get more information on the topic of Sound Waves at The Physics Classroom Tutorial.