Questions: Enrico is standing in a very cold day (it is 2°C) and he yelled and he hears sound waves reflected off a mountain nearby and come back to him 8 seconds later. Enrico wants to know how far is that mountain from him.

Solution Steps

We are given:

• Temperature: \(2^{\circ} \mathrm{C}\)
• Time for the sound to travel to the mountain and back: 8 seconds

The speed of sound in air can be approximated using the formula: \[ v = 331.3 + 0.606 \cdot T \] where \( T \) is the temperature in degrees Celsius.

Substituting \( T = 2 \): \[ v = 331.3 + 0.606 \cdot 2 \] \[ v = 331.3 + 1.212 \] \[ v = 332.512 \, \text{m/s} \]

The total time for the sound to travel to the mountain and back is 8 seconds. Therefore, the time to travel one way is: \[ t = \frac{8}{2} = 4 \, \text{s} \]

Using the formula for distance: \[ d = v \cdot t \] Substituting the values: \[ d = 332.512 \, \text{m/s} \cdot 4 \, \text{s} \] \[ d = 1330.048 \, \text{m} \]

Final Answer