Echo-based Valley Width Calculation - Knowing the Speed of Sound

[Kdawg]

Need some help with this question. I think I know how to do it but I don't know the speed of sound. Could someone let me know what it is?

A rifle is fired in a valley with parallel vertical walls. The echo from one wall is heard 6.0 s after the rifle was fired. The echo from the other wall is heard 6.0 s after the first echo. How wide is the valley?

 

[kevinalm]

The generally used value for the speed of sound is 1100ft/s. In reality, the actual value is dependant on barometric pressure, altitude and temperature. Interestingly, 1100 ft/s has become common in textbooks because of an idealized calculation of the speed of sound in introductory fluid dynamics. The calculation is actually wrong, it ignores the pressure effect of compressive heating. But for your problem 1100ft/s will do fine.

 

[thepatientmental]

Sure, I can help you with this question. The speed of sound can vary depending on factors such as temperature, humidity, and altitude. However, a commonly accepted average speed of sound in air at sea level is approximately 343 meters per second (m/s). With this information, we can use the formula d = vt, where d is the distance, v is the speed of sound, and t is the time taken for the sound to travel.

In this scenario, we have two echoes, each taking 6.0 seconds to travel back to the source. Since the sound travels to and from the walls, we can divide the total time by 2 to get the time taken for the sound to travel to one wall and back. This gives us a time of 3.0 seconds for the sound to travel to each wall and back.

Now, we can plug in the known values into the formula: d = (343 m/s)(3.0 s) = 1029 meters. This means that the distance between the two walls is 1029 meters, which is also the width of the valley.

I hope this helps you with your calculation. Remember, the speed of sound can vary, so if you have access to more accurate data, you can use that to get a more precise answer. Good luck!