# Rock off cliff - calculate height by using speed of sound

• Bikengine
In summary, to find the height of the fog-shrouded cliff in the High Sierra, you dropped a rock from the top and heard the sound of it hitting the ground after 8.50 seconds. Using the formula for distance, you can calculate the height of the cliff by taking into account the time it took for the sound of the rock hitting the ground to reach you. By ignoring air resistance and knowing the speed of sound is 330 m/s, you can determine the height of the cliff.
Bikengine
You are climbing in the High Sierra where you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top and 8.50s later hear the sound of it hitting the ground at the foot of the cliff.

Ignoring air resistance, how high is the cliff if the speed of sound is 330 m/s?

v = u + at
s = ut + 1/2at^2
d = st

I am confused because the rock takes 8.5 secs to fall, and I can't figure out how to determine at what point in those 8.5 seconds the rock hits the bottom, and the sound of it starts traveling up to the top of the cliff

Bikengine said:
I am confused because the rock takes 8.5 secs to fall, and I can't figure out how to determine at what point in those 8.5 seconds the rock hits the bottom, and the sound of it starts traveling up to the top of the cliff
The 8.5 s refers to the time that you hear the rock hit the bottom. So the time for the rock to hit the bottom, t1, is less than 8.5s and the remaining (8.5 - t1)s is the time for the sound of the rock hitting the bottom (or echo) to reach you.

1 person
I have the answer now, thanks very much!

## What is the speed of sound?

The speed of sound is the rate at which sound travels through a medium, such as air or water. In dry air at 20 degrees Celsius, the speed of sound is approximately 343 meters per second.

## How does the speed of sound help calculate the height of a cliff?

The speed of sound can help calculate the height of a cliff by using the time it takes for a sound wave to travel from the top of the cliff to the bottom and back up. This time, along with the speed of sound, can be used to calculate the distance the sound wave traveled, which is equal to the height of the cliff.

## What is the formula for calculating the height of a cliff using the speed of sound?

The formula for calculating the height of a cliff using the speed of sound is height = (speed of sound * time)/2. This formula is based on the fact that the sound wave travels down to the bottom of the cliff and back up, so the distance traveled is equal to twice the height of the cliff.

## Are there any factors that may affect the accuracy of this calculation?

Yes, there are a few factors that may affect the accuracy of the calculation. These include changes in temperature, wind speed, and humidity, which can all affect the speed of sound. In addition, the accuracy of the time measurement and the assumption that the sound wave travels straight down and back up may also impact the accuracy of the calculation.

## What are some other methods for calculating the height of a cliff?

Other methods for calculating the height of a cliff include using a measuring tape or ruler, using a rangefinder or laser distance measurer, or using trigonometry and a measuring tool to calculate the angle of elevation from a known distance away from the base of the cliff. Each method may have its own limitations and potential sources of error.

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