how many seconds will elapse between seeing lightning and hearing the thunder if the lightning strikes miles away and the temperature is 100.0 degrees F?
The sound velocity depends on temperature as
v (meters per second)=20.046•sqroot(T)
where T is absolute temperature (in Kelvins),
or
v(meters per second) = 331.4+0.6•t,
where t is the temperature in degrees centigrade
100F = 37.78 degrC
v = 331.4+0.6 •37.78=354.06 m/s.
1 mile =1 609 m.
t = s/v = 1 609/354.06 =4.54 s
What is the actual formula you are using? I cannot tell what you mean when you say "v=331.4 +0.6t". I want to actually learn how to do it.
That is the actual formula, worth memorizing. Vsound= 331.4+.6T, T in Celcius.
To determine the number of seconds that will elapse between seeing lightning and hearing thunder, we need to consider the speed of sound and the speed of light.
First, let's determine the speed of sound at the given temperature of 100.0 degrees F. The speed of sound can be estimated using the approximate formula:
speed of sound (in feet per second) = 1086 * square root(1 + (temperature in degrees Fahrenheit - 32) / 492)
Plugging in the temperature of 100.0 degrees F into the formula, we have:
speed of sound = 1086 * square root(1 + (100 - 32) / 492)
≈ 1086 * square root(1 + 0.1378)
≈ 1086 * square root(1.1378)
≈ 1086 * 1.067
≈ 1159 feet per second
Keep in mind that this formula provides an approximate value for the speed of sound, and the actual speed may vary slightly under different conditions.
Now, we need to calculate the time it takes for the sound to travel from the lightning strike to the observer's location. We can use the following formula:
time (in seconds) = distance (in feet) / speed of sound (in feet per second)
To convert the distance in miles to feet, we multiply it by 5280 (1 mile = 5280 feet). Let's assume the distance between the observer and the lightning strike is "x" miles.
distance (in feet) = x * 5280
= 5280x feet
Plugging this value into the equation, we have:
time (in seconds) = (5280x) feet / 1159 feet per second
= (5280x) / 1159 seconds
≈ 4.554x seconds
Therefore, the number of seconds that will elapse between seeing lightning and hearing thunder is approximately 4.554 times the distance between the observer and the lightning strike, in miles.