Please help. I got 338.82 for the velocity and wanted to get the distance, but I can't seem to do it because I don't have the wavelength. Please help!

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.20 s later. Find the depth of the well if the air temperature is 12.0°C.

Here is a site that allows one to calculate the speed of sound in air at the desired temperature.

That is the correct speed, but I don't know how to find the depth of the well, which is what the question is asking for.

Here is a site that allows one to calculate the speed of sound in air at the desired temperature.http://www.sengpielaudio.com/calculator-speedsound.htm

Isn't distance = rate x time.
So multiply the speed of sound x 2.2 seconds = ??

Nope that doesn't give the right answer, but thanks lots for your help!

Make sure you have the right units. Do you know the answer? If speed is in meters/second then the distance will come out in meters.

I think you should take into account the time it takes for the stone to hit the water. If the distance is d, then the time needed for the stone to reach the water, t1, follows from:

1/2 g t1^2 = d ------->

t1 = sqrt(2 d/g)

The time needed for the sound to reach you is:

t2 = d/v

where v = 338.82 m/s is the speed of sound.

So, the total time is:

T = t1 + t2 = d/v + sqrt(2 d/g)

It is given that T = 2.20 s, so we get the equation:

d/v + sqrt(2 d/g) = 2.20 s

You can put d = x^2 to convert this to a quadratic equation. I find
d = 157.7 m (but I haven't double checked...)

To find the depth of the well, we can use the equation of motion for the stone and the equation for the speed of sound in air.

First, let's find the initial velocity (u) of the stone when it was dropped. We know that the stone was dropped from rest and didn't have any initial velocity, so u = 0.

The equation of motion for an object in free fall is:

s = ut + (1/2)gt^2

Where:
s is the distance traveled (which in this case is the depth of the well)
u is the initial velocity (0 in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken (2.20 s in this case)

Plugging in the values, we have:

s = 0 * 2.20 + (1/2) * 9.8 * (2.20)^2

Simplifying the equation, we get:

s = 0 + 0.5 * 9.8 * 4.84

s = 0 + 47.716

s = 47.716 meters

So, the depth of the well is approximately 47.716 meters.

Please note that the speed of sound in air is not needed to solve this particular problem. The sound of the splash is heard after a specific time period, but its speed doesn't affect the calculation of the depth of the well in this case.