# How far is the bat from the wall when it hears the echo?

• ohms law
In summary: I'll have to check it out.In summary, the conversation discusses the use of echo location by bats and a specific problem involving a bat flying towards a vertical cliff. The solution involves determining the bat's position and the time it takes for the sound to travel to the wall and back. The conversation also mentions a different solution method that takes into account the entire distance traveled.
ohms law

## Homework Statement

From Tipler & Mosca, Ch. 2, #56 (pg. 57)
Bats use echo location to place themselves. (I condensed all of this from the problem) So:
Bat flying at 19.5 m/s toward a vertical cliff.
Bat clicks.
Bat hears the echo 0.15 s later. (click travels at 343 m/s)

How close is the bat when it hears the echo?

## Homework Equations

The position function for the bat is straightforward: $X_{bat}=19.5t$
the position function for the sound takes a little reasoning. The sound has to travel to the wall and back, so I'm going with $X_{click}={1/2} * 343t$.

## The Attempt at a Solution

Solve these functions for t=0.15:
$X_{f bat}=19.5 m/s(0.15 s)=2.925 m$
$X_{click}={1/2} * 343 m/s(0.15 s)=25.725 m=X_{i bat}$

So, the bat's initial position is 25.725 m from the wall, and it's final position would be:
$X_{f bat}= X_{i bat} - X_{f bat} = 25.725 m - 2.925 m = 22.8 m$
So, the bat is 22.8 m from the wall when it hears the click.

The way I did this was putting both velocities into one equation:

$\frac{1}{2}$*(vSound - vBat)*t

Using this, I got the answer of 24.263, which is the answer that the book gives for this question. The only thing that is different from your methodology is the fact that the $\frac{1}{2}$ affects vBat as well.

Hey, thanks!
I didn't realize that the book gave an answer. I don't see one (and there isn't one in the SSM either).

Anyway... why would the velocity of the bat need to be halved? The sound has to travel to the wall and back, but the bat is traveling in a straight line (and at constant speed). So... wouldn't halving it's displacement mean that it hears the click instantaniously, when the click hits the wall?

It doesn't, but I was lucky enough to find all of the solution manuals http://spotcos.com/misc/UW_PHYS_12X_ANSWERS/ while looking for help on a problem one night.

The reason for the velocity of the bat being halved is due to solving everything as one set that takes into account how long the entire distance is; the position of the bat factors in twice when dealing with the entire distance as a variable. If you download the solution manual for chapter 2 from that link, a step-by-step process is given for this method.

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## What is the "Bat displacement problem"?

The "Bat displacement problem" refers to the issue of bats being displaced from their natural habitats due to human activities such as deforestation, urbanization, and construction.

## Why is bat displacement a problem?

Bat displacement is a problem because it can lead to a decline in bat populations and disrupt the balance of ecosystems. Bats play important roles in pollination and insect control, and their absence can have negative impacts on agricultural and ecological systems.

## How does bat displacement affect humans?

Bat displacement can indirectly affect humans by disrupting the balance of ecosystems, which can lead to changes in insect populations and crop yields. It can also directly affect humans by increasing the risk of disease transmission from bats to humans, as displaced bats may seek shelter in human structures.

## What are some solutions to the bat displacement problem?

Solutions to the bat displacement problem include creating and preserving bat-friendly habitats, implementing measures to reduce negative impacts of human activities on bat populations, and educating the public about the importance of bats and the consequences of their displacement.

## How can scientists help address the bat displacement problem?

Scientists can help address the bat displacement problem by conducting research on bat behavior, habitat preferences, and population trends to better understand the issue and inform conservation efforts. They can also collaborate with other experts and stakeholders to develop and implement effective solutions.

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