Vibrations and Waves Legacy Problem #8 Guided Solution
Problem*
Microbats use echolocation to navigate and hunt. They emit pulses of high frequency sound waves which reflect off obstacles and objects in their surroundings. By detecting the time delay between the emitted pulse and the return of the reflected pulse, a bat can determine the location of the object. Determine the time delay between the sending of a pulse and the return of its reflection from an object located 12.5 m away. Approximate the speed of the sound waves as 345 m/s.
Audio Guided Solution
The difficulties which students have with physics problems is varied, but for certain one of the difficulties is related to the tendency to rush into the calculator use without giving the situation much cognitive thought. Here we have a problem about bats which send out pulses in order to locate their prey. The pulses bounce off an object 12.5 meters away and return to the bat, traveling at 345 meters per second through the air. So what we have is a distance from bat to object and the speed at which that distance is traveled. But what we wish to do is calculate the time it takes for the pulse to go from the bat to the object and back to the bat. Thus the distance traveled by this pulse is not the 12.5 meters which is given, but rather twice that amount, 25.0 meters. After all, this time we are looking to calculate is not the time it takes for the pulse just to go from the bat to the prey, but to the bat to the prey and back. And so we need to use the equation V equals D over T, rearranged in order to solve for time. Rearranging it gives us T equals D divided by V. Taking the 25.0 meters and dividing by the 345 meters per second gives me 0.0725 seconds. Or if I wish to express this in milliseconds, I can move the decimal place three places to the right. It will be 72.5 milliseconds. Now if in this problem you got 0.03625ish or thereabouts seconds, then you likely suffered from the tendency to rush into your calculator too quickly before giving the problem much cognitive thought.
Solution
0.0725 seconds (72.5 milliseconds)
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.
Read About It!
Get more information on the topic of Vibrations and Waves at The Physics Classroom Tutorial.