you visit the grand canyon on a particularly hot day and like all good tourists, you yell, Hello! Would you expect to hear the echo sooner or later than on a cooler day? Why?
please show all work
Thank you
To determine whether you would expect to hear the echo sooner or later on a particularly hot day at the Grand Canyon compared to a cooler day, we need to discuss the factors that influence the speed of sound.
The speed of sound depends on the temperature of the air. As the temperature increases, the speed of sound also increases. This is because at higher temperatures, air molecules move faster, resulting in faster propagation of sound waves.
Now, let's analyze the scenario:
1. On a particularly hot day:
Since the temperature is higher, the speed of sound is also expected to be higher. This means that sound waves will travel faster through the hot air.
2. Echo formation:
An echo occurs when sound waves bounce off a surface and return back to the source. In the case of yelling at the Grand Canyon, the sound waves will reflect off the canyon walls and travel back to the person who yelled.
Based on the factors mentioned above, you would expect to hear the echo sooner on a particularly hot day compared to a cooler day. This is because the sound waves will travel at a higher speed through the hotter air, allowing them to reach the person faster.
To further support this conclusion, we can consider the formula for the speed of sound in dry air, which is approximately:
v = 331.4 + 0.6 * T
Where:
v = speed of sound in meters per second
T = temperature in degrees Celsius
As the temperature T increases, the speed of sound v also increases. Therefore, on a particularly hot day, the speed of sound will be higher, leading to a quicker arrival of the echo.