Describe an echo as the reflection of sound waves

3.4 Sound – Echo

Learning Objective

Describe an echo as “a distinct, audible repetition of a sound” that results from the reflection of sound waves, explain the conditions required for an echo to be heard, and use the relevant equations to calculate distances and speeds.

1. Production of Sound (Syllabus Requirement)

• Vibrating source: Any object that vibrates (e.g., a tuning‑fork, a speaker diaphragm) creates periodic compressions and rarefactions in the surrounding medium.
• Longitudinal wave: Particles of the medium oscillate parallel to the direction of wave travel, producing a longitudinal pressure wave.
• Audible frequency range: Human‑audible sound lies approximately between 20 Hz and 20 kHz. The range is an approximation; extreme low or high frequencies are difficult for many people to hear – a useful reminder for AO1.

2. Definition of an Echo (Syllabus Wording)

An echo is a distinct, audible repetition of a sound that occurs when the sound wave is reflected from a surface and returns to the listener after a measurable delay.

3. How an Echo Is Formed

1. A sound source generates a longitudinal wave that propagates through a medium (normally air).
2. The wave reaches a reflecting surface (wall, cliff, building, etc.).
3. Part of the incident wave is reflected; the reflected wave travels back toward the source.
4. If the reflected wave arrives at the listener after a sufficient delay, it is heard as a separate sound – the echo.

4. Conditions Required for an Audible Echo (Syllabus Requirement)

Condition	Explanation (syllabus‑aligned)
Large, smooth reflecting surface	Must be big enough to intercept a significant portion of the incident wave and smooth enough to return a noticeable fraction of the sound energy.
Minimum round‑trip time ≥ 0.1 s	The ear can separate two sounds only if they are at least 0.1 s apart. This is a *minimum*; longer distances also produce audible echoes.
Medium continuity	The medium (usually air) must be continuous. Strong temperature gradients, wind, or turbulence can refract or attenuate the wave.
Surface size (large enough)	Related to the first condition – a surface that is too small reflects only a weak portion of the wave, making the echo inaudible.

5. Why 0.1 s?

The human auditory system can discriminate two separate sounds only when the interval between them is ≥ 0.1 s. Using the typical speed of sound in air (≈ 340 m s⁻¹):

\[ d_{\text{min}}=\frac{v \times 0.1\ \text{s}}{2}\approx\frac{340\times0.1}{2}=17\ \text{m} \]

Thus a reflecting surface must be at least about 17 m away for the echo to be heard as a distinct sound.

6. Speed of Sound (Syllabus Requirement)

• Typical value in dry air at 15 °C: \(v \approx 340\ \text{m s}^{-1}\).
• Dependence on medium: Solids > Liquids > Gases (fastest in solids).
• Temperature dependence (air): \[ v = v_{0}\sqrt{1+\frac{T}{273}}\qquad\text{with }v_{0}=331\ \text{m s}^{-1}\text{ at }0^{\circ}\text{C}, \] where \(T\) is the temperature in °C.
• Example calculation: At 25 °C, \[ v = 331\sqrt{1+\frac{25}{273}} \approx 331\sqrt{1.0916} \approx 331\times1.045 \approx 346\ \text{m s}^{-1}. \]

7. Measuring the Speed of Sound Using the Echo Method

1. Place a loudspeaker (or a starter pistol) at a known distance \(d\) from a large, flat wall.
2. Emit a short, sharp pulse.
3. Measure the time interval \(t\) between the original pulse and its echo with a stopwatch, timer, or oscilloscope.
4. Calculate the speed using \[ v = \frac{2d}{t}. \]

8. Calculating Distance to a Reflecting Surface

If the measured round‑trip time is \(t\), the distance to the surface is

\[ d = \frac{v\,t}{2}. \]

• Note: \(t\) is the *round‑trip* time (outward + return), not the one‑way travel time.
• \(v\) must be the speed of sound appropriate for the temperature and medium.

9. Factors Affecting Echo Intensity

1. Surface material: Hard, smooth materials (concrete, stone, metal) reflect more sound than soft, porous ones (curtains, foliage).
2. Surface size: Larger surfaces intercept a greater fraction of the incident wave, producing a louder echo.
3. Angle of incidence: The law of reflection (\(\theta_i = \theta_r\)) applies. Very shallow angles may cause the reflected wave to miss the listener.
4. Atmospheric conditions: Temperature, humidity, and wind can change the speed of sound and refract the wave, altering both delay and intensity.

Suggested classroom activity (AO3): Using a sound‑level meter, measure the intensity of an echo from three different surfaces (e.g., brick wall, wooden door, thick curtain) at the same distance. Record the decibel values and discuss how material and size affect the results.

10. Everyday Examples of Echoes

• Shouting into a canyon and hearing the sound return.
• Clapping in a large, empty hall or gymnasium.
• Sonar on ships and submarines – sound pulses are sent out and the echo time is used to locate objects underwater.
• Medical ultrasound: High‑frequency sound pulses are reflected from body tissues; the time taken for the echo to return forms an image of internal structures.

11. Common Misconceptions (Syllabus)

• Echo vs. reverberation: Reverberation is a rapid series of overlapping reflections that blend with the original sound; an echo is a single, clearly separated reflection.
• All reflections are echoes: Only reflections arriving ≥ 0.1 s after the original are perceived as echoes.
• “An echo can be heard from any distance”: The 0.1 s limit means that surfaces closer than about 17 m (in air at 340 m s⁻¹) produce a reflection that is heard as part of the original sound, not as a distinct echo.

12. Summary

An echo is the audible reflection of a longitudinal sound wave from a large, smooth surface. It is heard as a distinct repetition when the round‑trip travel time is at least 0.1 s (≈ 17 m in air at 340 m s⁻¹). The distance to the reflecting surface can be found with \(d = \dfrac{v t}{2}\), where \(t\) is the measured round‑trip time. The intensity of an echo depends on the material, size, orientation of the surface and on atmospheric conditions. Mastery of sound production, the speed‑of‑sound formula (including temperature correction), and the echo method equips students to solve AO1–AO3 exam questions.

13. Practice Questions

1. A person shouts toward a cliff and hears an echo 0.6 s later. Calculate the distance to the cliff. (Assume \(v = 340\ \text{m s}^{-1}\).)
2. Explain why an echo is not heard when shouting at a wall only 5 m away.
3. Describe how an increase in air temperature from 15 °C to 25 °C affects the speed of sound and the measured time delay of an echo from a fixed wall.
4. Using the echo method, a student measures a round‑trip time of 0.30 s for a wall 50 m away. Determine the experimental speed of sound and comment on possible sources of error.
5. Calculate the speed of sound at 25 °C using the syllabus temperature formula and then find the expected echo time for a wall 30 m away. Compare this with the time you would obtain if you incorrectly used \(v = 340\ \text{m s}^{-1}\).