Solving a Sound Wave Problem: Distance to Target

[Banana]

Banana states: I need help setting this problem up: A person fires a rifle horizontally. The bullet has a muzzel speed of 200 m/s, and the person hears the bullet strike the target 1 second after firing. The air temp is 72 degrees Farenheit. What is the distance of the target? (I know to convert to 22.2 degrees C, and I then found the speed of sound at this temp. I got 344.3 m/s. But where does the bullet's velocity come in? I don't think this is a Doppler effect problem, because we didn't get to that section yet.) Can anyone get me started in the right direction?

 

[gnome]

I think the bullet's speed is there to make you think about what information you really need in order to solve this problem.

So, how do YOU think you can solve this?

(I get 344.2 m/s, by the way.)

 

[Banana]

I have a solution manual, but it won't do me any good if I don't understand what they did, and I don't really understand. I'm trying to reason it out for myself. They add 1/sound velocity + 1/bullet velocity, and that sum is the denominator with 1 second being the numerator. Doing that will get me the right answer, but I want to understand why they did that. (I notice that I seldom set up problems the way the solution manual does)

 

[Doc Al]

Think it through step by step: What has to happen before the person firing the rifle hears the sound made by the bullet striking the target? Draw yourself a picture of what is happening, and when it happens.

I'll start you off. The first thing that happens is that the bullet leaves the rifle! What's next?

 

[Banana]

It seems that the gun is between the person and the target, so wouldn't the sound wave travel the opposite direction than the bullet?

 

[Banana]

Or does the sound wave go to the target and bounce back? I'm so clueless I'm not even sure if the bullet hits the target before or after the sound is heard.

 

[gnome]

You're not dealing with a sound wave that makes a "round trip". NOT the sound of the gun firing. Just the sound of the bullet hitting the target. That sound wave doesn't exist at all before the bullet gets to the target, right?

Assume the person & the gun are at exactly the same location. The person doesn't know when the bullet strikes the target.

The person does know:
. the time when the bullet started its trip
. the time when the sound arrived (in other words, when the sound ended its trip)
. the speed of the bullet
. the speed of the sound

 

[Doc Al]

Originally posted by Banana
Or does the sound wave go to the target and bounce back? I'm so clueless I'm not even sure if the bullet hits the target before or after the sound is heard.

The sound talked about is the sound of the bullet hitting the target. Think of the target as a bell which the bullet rings when it hits it. Before the bullet gets to the target there is no sound! (At least no sound of the bell!)

The events are:
1) bullet leaves gun (location A)
2) bullet hits target (location B) --- creates sound, which spreads out
3) sound arrives back at location A, where the person hears it.

We want to figure out the distance between A and B.

 

[Banana]

Does the solution manual's set up make sense to you? Why would you know to make the two velocities demoninators? Grrr. I'm frustrated.

 

[Doc Al]

Originally posted by Banana
Does the solution manual's set up make sense to you? Why would you know to make the two velocities demoninators? Grrr. I'm frustrated.

Use the formula: Distance = Speed x Time

You are trying to find the distance between A (person) and B (target); call that distance "D" and use what you know (and the formula) to find the following.

Find the time it takes for the bullet to get from the gun (A) to the target (B).
Find the time it takes for the sound to get from the target (B) back to the person (at A).

These two times must add up to what?

 

[Banana]

Thank you, I finally get it!