Class 10 > Unit # 11: Sound > Methods to determine Speed of Sound

Methods to Determine the Speed of Sound in Air

The speed of sound in air can be practically measured using two simple direct experimental methods:

Method 1: Direct Measurement Between Two Points

This method measures the time taken for a sound wave to travel directly across a measured distance between two observers.

Procedure:

1. Two observers stand a direct distance apart in an open field, at a distance of at least 100 meters.
2. The exact distance (\(d\)) between them is measured accurately using a trundle wheel or measuring tape.
3. The first person holds two wooden blocks (or visual sound sources) high above their head and bangs them together sharply to produce a loud sound.
4. The second person, holding a stopwatch, starts timing the instant they see the wooden blocks strike each other (or upon visual signal) and stops the timer when they hear the clap. Alternatively, to reduce human reaction time error, the time for 20 repeated claps is measured continuously.
5. The experiment is repeated several times to calculate an average value for the time (\(t\)).
6. The speed of sound (\(v\)) is then calculated using the standard formula:

$$\text{Speed of Sound } (v) = \frac{\text{Distance } (d)}{\text{Time } (t)}$$

Sample Calculation:

If distance \(d = 120\text{ m}\) and average time taken \(t = 0.35\text{ s}\):

$$v = \frac{120\text{ m}}{0.35\text{ s}} \approx 342.8\text{ m/s}$$

Method 2: Using Echoes (Reflection Method)

This method utilizes sound reflection from a hard flat surface, such as a large wall or cliff face.

Procedure:

1. A person stands at a measured distance (\(d\)) of approximately 50 meters away from a large wall or cliff face using a trundle wheel.
2. The person claps two wooden blocks together and listens for the returning echo reflecting off the wall.
3. The person then begins clapping the blocks repeatedly at a steady rhythm so that each clap coincides exactly with the echo of the previous clap.
4. A second person with a stopwatch starts timing when the rhythmic clapping begins and stops the watch after 20 claps.
5. The experiment is repeated multiple times to obtain an accurate average time (\(t\)).
6. Since the sound wave travels to the wall and bounces back, the distance covered for each clap-echo pair is \(2 \times d\). The total distance for 20 claps is \(20 \times 2 \times d\).
7. The speed of sound (\(v\)) is calculated using the relation:

$$\text{Speed of Sound } (v) = \frac{2 \times \text{Distance to Wall } (d)}{\text{Time for one echo } (t)}$$
$$\text{Or for } N \text{ claps: } v = \frac{N \times 2 \times d}{\text{Total Time } (t_{\text{total}})}$$

Sample Calculation:

If distance to wall \(d = 50\text{ m}\) and time for 1 echo \(t = 0.28\text{ s}\):

$$v = \frac{2 \times 50\text{ m}}{0.28\text{ s}} = \frac{100\text{ m}}{0.28\text{ s}} \approx 357.1\text{ m/s}$$