Sound Waves Legacy Problem #6 Guided Solution
Problem*
A deep-sea ocean vessel uses SONAR to detect the ocean's bottom. Sound waves are emitted from the surface of the ocean and travel through the water at 1450 m/s. The ocean bottom is 1630 m below the surface. Determine the amount of time that passes before the sound waves are reflected back to the surface.
Audio Guided Solution
A good problem solver reads the problem carefully and develops a mental picture of what's going on, maybe even diagrams the situation. Here as I read this problem, the mental picture that I get is of a boat, ship on top of the ocean water, in an ocean bottom, and waves that are traveling from the ocean surface down to the bottom and back up. What I wish to calculate is the time that passes before the sound waves are reflected back to the surface from the ocean bottom. So there's a two-way trip, down and back, and what I want to calculate is the time for that down and back trip. What I have is the speed of these sound waves to the water, and what I also have is I have the distance from the surface to the ocean's bottom. That's not actually the distance I'm going to directly use in my equation that I pick, but that's the distance, one way, from the ocean surface to the ocean bottom. Now the equation I'm going to use to calculate time is the definition of speed, speed equal distance divided by time. I want to take that equation and rearrange it to solve for time. So what I'm going to do is multiply both sides of the equation by t, and then the equation becomes v times t is equal to d, the v there is the speed, and then I'm going to divide each side of the equation by v, and that gives me t equals d divided by v, and now I can substitute. In the denominator first, I'm going to put the v, the speed of the sound waves, it's 1450 meters per second, but in the numerator, since I wish to calculate the time down and back, I'm going to have to put the distance down and back, which is going to be twice the 1630 meters. So I go two times 1630 meters, that gives me my numerator, I divide by 1450 meters per second, and that gives me a time of 2.2483 seconds, and I can round that to three significant digits.
Solution
2.25 s
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.