Calculating Depth & Distance (Edexcel GCSE Physics)

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Calculating Depth & Distance

Higher Tier Only

  • If the speed of a wave is known, it can be used to calculate the distance to an object, or the depth of an object - say, underwater

Calculating Distance

  • The worked example below demonstrates how the speed of sound in air can be used to determine how far away objects are from an observer

Worked example

A clap of thunder is heard 4 seconds after the corresponding flash of lightning.How far away is the thunderstorm? (The speed of sound in air is 330 m/s) 

Step 1: List the known quantities

    • Wave speed, v330 m/s
    • Time, t = 4 s

Step 2: Write out the wave speed, distance and time formula 

Step 3: Re-arrange the equation to make distance (x) the subject

x = v × t

Step 4: Put known values into the equation

x = 330 × 4 = 1320 m

    • So the distance to the thunderstorm is 1320 m

Calculating Depth

  • Echo sounding uses ultrasound to detect objects underwater
  • The sound wave is reflected off the ocean bottom
  • The time it takes for the sound wave to return is used to calculate the depth of the water
  • The distance the wave travels is twice the depth of the ocean
    • This is the distance to the ocean floor plus the distance for the wave to return

Echo Sounding, downloadable IGCSE & GCSE Physics revision notes

Echo sounding is used to determine water depth

Worked example

The sound wave released from a ship took 0.12 seconds to return. The speed of sound in water is 1500 m/s.What was the depth of the sea? 

Step 1: List the known quantities

    • Wave speed, v = 1500 m/s
    • Time, t = 0.12 s

Step 2: Write out the wave speed, distance and time formula

Step 3: Rearrange the equation to make distance (x) the subject

x = v × t

Step 4: Put known values into the equation

x = 1500 × 0.12 = 180 m

Step 5: Half the distance to obtain the depth

d = 180 ÷ 2

Depth, d = 90 m

Examiner Tip

Don't forget to take into account if a sound wave has travelled twice the distanceYou can do this one of two ways:

  • Halve the time at the beginning, or
  • Halve the distance at the end

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.