A rifle is fired in a valley with parallel vertical walls. The echo from one wall is heard 1.0s after the rifle was fired. The echo from the other wall is heard 1.0s after the first echo. How wide is the valley?

Yes, I am supposed to use 343 m/s so:

(343)(1)(.5)+(343)(2)(.5)=514.5 m/s

Looks ok to me. However, if your prof is concerned about significant figures, (some are, some aren't), you have only two with 1.0 seconds so you need to round the answer.

Look up the speed of sound at the conditions in the valley. At sea level I found about 340 m/s but use the speed you find.

It took 1.0 sec for the echo from the first wall which means the distance from the rifle to the first wall is 340 m/s * 1 sec * 1/2 = ?? (the sound had to travel there AND back. The distance from the rifle to the second wall was
340 m/s * 2 sec * 1/2 = ??
Add the two together to obtain the distance between the two walls. Check my thinking.

To find the width of the valley, we need to consider the time it takes for the sound to travel from the rifle to the first wall, from the first wall to the second wall, and from the second wall back to the observer.

Let's break down the timeline of events:

1. The rifle is fired.
2. The sound from the rifle travels to the first wall, creating an echo.
3. The echo from the first wall travels back to the observer.
4. The sound from the first wall reaches the second wall, creating another echo.
5. The echo from the second wall travels back to the observer.

Given that the echo from one wall is heard 1.0s after the rifle was fired, and the echo from the other wall is heard 1.0s after the first echo, we can conclude that the total time it takes for the sound to travel to the second wall and back is 2.0s.

Now, the speed of sound can be considered constant at approximately 343 meters per second in dry air at 20 degrees Celsius. To find the width of the valley, we need to calculate the total distance the sound traveled.

Since the sound traveled to the first wall and back, we can calculate this distance using the formula:
Distance = Speed x Time

Distance to and from the first wall = 343 m/s x 1.0 s = 343 meters.

Since the sound traveled to the second wall and back, we can calculate this distance using the same formula:
Distance to and from the second wall = 343 m/s x 2.0 s = 686 meters.

Since the width of the valley is the sum of the distances to and from each wall, we add the two distances together:
Width of the valley = Distance to and from the first wall + Distance to and from the second wall
= 343 meters + 686 meters
= 1029 meters.

Therefore, the width of the valley is 1029 meters.