IGCSE Physics 0625

3.4 Sound - Echoes

An echo is a sound wave that is reflected back to the listener after it has traveled from a source. It is a direct result of sound waves bouncing off surfaces.

How Echoes Form

1. A sound wave is produced by a source (e.g., a person speaking, an instrument playing).
2. The sound wave travels through a medium (e.g., air) in all directions.
3. When the sound wave encounters a solid surface (e.g., a wall, a mountain), some of the sound energy is reflected.
4. The reflected sound wave travels back to the listener.
5. The listener perceives the reflected sound wave as an echo, arriving with a slight delay after the original sound.

Factors Affecting Echoes

The clarity and loudness of an echo depend on several factors:

• Distance to the reflecting surface: The further the surface is, the longer it takes for the reflected sound to return, and the clearer the echo will be.
• Size and shape of the reflecting surface: Larger, flatter surfaces tend to reflect sound more effectively.
• Material of the reflecting surface: Hard, smooth surfaces (like concrete or glass) reflect sound better than soft, rough surfaces (like fabric or carpet).
• Temperature and humidity of the air: These factors can affect the speed of sound, which in turn can slightly alter the timing of the echo.

Mathematical Relationship

The time it takes for a sound wave to travel to a reflecting surface and back is crucial for hearing an echo. This time can be calculated using the following formula:

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

Where:

• t is the total time taken for the sound wave to travel to the surface and back (in seconds).
• d is the distance between the sound source and the reflecting surface (in meters).
• v is the speed of sound in the medium (in meters per second). The speed of sound in air is approximately 343 m/s at room temperature (around 20°C).

Example

Consider a person standing 10 meters from a large wall. The time it takes for the sound of their voice to reach the wall and return is:

$$ t = \frac{2 \times 10}{343} \approx 0.058 \text{ seconds} $$

This short delay is enough for the person to perceive the sound as a distinct echo.

Factor	Effect on Echo
Distance to Reflecting Surface	Greater distance leads to a clearer echo.
Size and Shape of Surface	Larger, flatter surfaces reflect sound better.
Material of Surface	Hard, smooth surfaces reflect sound better.
Temperature and Humidity	Can slightly affect the speed of sound and the timing of the echo.