4.8P Calculate depth or distance from time and wave velocity

The idea

This specification point asks you to use the wave equation in the form distance = wave velocity × time, written d = v × t, to find how far a wave travels or how deep a reflecting surface lies. Identify the wave velocity v in metres per second and the time t in seconds, then multiply them. For an echo or pulse that travels out and back, the measured time covers the whole journey, so halve it before calculating a one-way depth: a sonar pulse in water at 1500 m/s returning after 0.40 s gives d = 1500 × 0.20 = 300 m. Convert milliseconds to seconds and kilometres to metres first, and give the answer with a unit.

What earns the marks

• Selects the relationship distance = wave velocity × time and substitutes the stated velocity and time correctly.
• Converts the time to seconds and the velocity to metres per second before multiplying.
• Halves a total echo time to obtain the one-way distance or depth.
• States the final answer with the correct unit and a sensible number of significant figures.

Common mistakes and how to put them right

• Uses the full echo time as a one-way time.

  Put it right: Halve the measured time before calculating depth.

• Multiplies without converting milliseconds to seconds.

  Put it right: Convert every quantity to SI units first.

• Omits the unit from the final answer.

  Put it right: Attach metres or the appropriate unit to the result.

Exam tips

• Write down d = v × t before substituting any numbers so the method is visible.
• Check whether the time is a total there-and-back journey and halve it if so.
• Convert all values to metres and seconds, then state the unit with your answer.