How to Calculate Depth or Distance from Time and Wave Velocity?

To calculate depth or distance from time and wave velocity, you use the fundamental relationship between speed, distance, and time. This is typically done by rearranging the formula for wave speed.

Understanding the Relationship

The speed of a wave describes how quickly it travels through a medium. This is directly related to the distance the wave covers and the time it takes to cover that distance. The basic formula connecting these quantities is:

Wave Speed = Distance / Time

Or, using variables:

• v = wave speed
• x = distance or depth
• t = time

v = x / t

The Formula for Distance

To find the distance (or depth), you need to rearrange this formula to make x the subject.

Starting with:
v = x / t

Multiply both sides by t to isolate x:

v × t = x

So, the formula to calculate distance or depth is:

Distance (x) = Wave Velocity (v) × Time (t)

Step-by-Step Calculation

Here's how to apply the formula, following the steps outlined in the reference:

1. List the known quantities: Identify the wave speed (v) and the time (t) the wave traveled.
   • Example from reference: Wave speed, v = 330 m/s. Time, t = 4 s.
2. Write out the wave speed, distance, and time formula: Understand the relationship v = x / t.
3. Re-arrange the equation to make distance (x) the subject: As shown above, this gives you x = v × t.
4. Put known values into the equation: Substitute the values of v and t that you listed in Step 1 into the rearranged formula and calculate x.
   • Example from reference: x = 330 m/s × 4 s = 1320 m.

Therefore, based on the example provided, a wave traveling at 330 m/s for 4 seconds covers a distance of 1320 meters.

This method is commonly used in various fields, such as:

• Sonar and Echo Sounding: Measuring water depth or locating underwater objects by sending out sound waves and timing how long the echo takes to return (though this involves round-trip time, which requires dividing the total time by two before using the formula above for one-way distance).
• Seismology: Determining the distance to an earthquake's epicenter using the travel times of seismic waves.
• Ultrasonography: Creating images of internal body structures based on the travel time of sound waves.