Measuring the Speed of Sound

The speed of sound in air can be measured using timing methods. Two common approaches are the direct-timing method and the echo method.

Method 1: direct timing with two observers

1. Two observers stand a known distance apart (e.g. 400 m).
2. Observer A makes a loud sound (e.g. clapping blocks, starting pistol).
3. Observer B starts a stopwatch when they see the action (light is effectively instant) and stops it when they hear the sound.
4. Calculate: $v = d / t$.

Improvement: repeat several times and take an average. Use a large distance to reduce the percentage error in the time measurement.

Method 2: echo method

1. Stand a known distance $d$ from a large flat wall.
2. Clap at a steady rhythm that coincides with the returning echoes.
3. Time $n$ clap intervals using a stopwatch.
4. The sound travels to the wall and back, so the total distance for one echo is $2d$.

$v = \frac{2d \times n}{t}$

where $t$ is the total time for $n$ echoes.

Worked example: echo method

A student stands 50 m from a wall and records 20 echoes in 5.9 s. Calculate the speed of sound.

Each echo involves a round trip of $2 \times 50 = 100$ m.

$v = \frac{100 \times 20}{5.9} = \frac{2000}{5.9} = 339\text{ m/s}$

Sources of error

• Reaction time of the observer (significant for short distances).
• Wind affecting the travel time of sound.
• The wall not being perfectly flat, causing scattered echoes.

Common errors and how to correct them

Forgetting to double the distance for echoes. The sound travels to the wall and back, so the distance is $2d$, not $d$.

Using too short a distance, making reaction time a large percentage of the measured time. Use at least 50 m for echo methods and 200 m or more for direct timing.

How to apply this in an exam

State the method, the measurements taken, the equation used, and how to improve accuracy (repeat and average, use a large distance). If describing the echo method, explicitly state the distance is doubled.