Chloe at the concert

This activity allows students to understand the relationship between sound level and distance from the source. It raises awareness of the hearing risks linked to exposure to high sound levels.

Imagine standing right in front of the speakers at a rock concert, where the sound level can reach 110 decibels or more, enough to cause permanent hearing damage in minutes. Now take ten steps back. How much quieter does it get? The answer involves one of the most universal laws in physics: the inverse square law. As sound radiates outward from a source, its energy spreads over an ever-increasing spherical surface, causing the intensity to drop with the square of the distance. This means that doubling your distance from a speaker reduces the sound intensity by a factor of four, corresponding to a 6 dB decrease. Understanding this relationship is not just an academic exercise; it has direct implications for hearing health. The World Health Organization estimates that over a billion young people are at risk of hearing loss from recreational noise exposure. This experiment gives students a quantitative framework for understanding how distance provides natural protection from loud sound sources, while reinforcing fundamental concepts in wave physics and logarithmic scales.

Learning objectives:

The student uses two smartphones to measure the impact of distance on sound level: one emits white noise via FizziQ's sound library while the other measures the noise level at different distances. By comparing the measurements and analyzing the differences observed, the student checks whether the initial statement is correct and reflects on the implications in terms of hearing health.

Level:

High school

FizziQ

Author:

Duration (minutes) :

35

What students will do :

- Measure sound level at multiple distances from a source and record the data systematically
- Verify the inverse square law for sound propagation: doubling the distance reduces the level by approximately 6 dB
- Understand the logarithmic nature of the decibel scale and its relationship to perceived loudness
- Evaluate the hearing risks associated with proximity to loud sound sources
- Apply the formula L = L₀ - 20 × log(d/d₀) to predict sound levels at various distances

Scientific concepts:

- Sound propagation
- Logarithmic decibel scale
- Relationship between sound power and distance
- Hearing health
- Risks linked to high intensity sounds

Sensors:

- Microphone (sound level meter in dB)

What is required:

- Two smartphones with the FizziQ application
- A quiet space for measurements
- A tape measure to precisely measure distances
- FizziQ experience notebook

Experimental procedure:

Set up the experiment in a quiet, open space with minimal reflections (outdoors is ideal; indoors, choose a large room away from walls).
On the first smartphone, open FizziQ and use the Sound Library or Synthesizer to emit white noise at a constant, moderate volume.
Place the emitting smartphone on a stable surface at a fixed position. This is your sound source.
On the second smartphone, open FizziQ and select the Sound Level (dB) sensor.
Measure and mark distances of 0.25 m, 0.50 m, 1.0 m, 1.5 m, 2.0 m, 3.0 m, and 4.0 m from the source using the tape measure.
Place the measuring smartphone at 0.25 m from the source. Record the sound level for at least 10 seconds and note the average value.
Repeat the measurement at each marked distance, always waiting for the reading to stabilize and recording for at least 10 seconds.
Enter all data pairs (distance, sound level) into your FizziQ notebook.
Plot the graph of sound level (dB) versus distance (m). The curve should decrease steeply at first, then more gradually.
Now plot sound level versus log(distance). This graph should be approximately linear with a slope close to -20 dB per decade (a factor of 10 in distance).
Verify the 6 dB rule: compare the sound level at 1 m and 2 m. The difference should be approximately 6 dB.
Using your measurements, calculate the minimum safe distance from a speaker producing 110 dB to stay below the 85 dB safety threshold.

Expected results:

Students should observe a clear decrease in sound level with increasing distance. For an ideal point source, each doubling of distance should produce a drop of approximately 6 dB. In practice, reflections from walls, floor, and ceiling will reduce this drop slightly (typically 4-5 dB per doubling indoors versus the theoretical 6 dB). The plot of sound level versus log(distance) should be approximately linear. At very short distances (under 25 cm), near-field effects may cause deviations from the inverse square law. Background noise will set a lower limit on measurable sound levels, typically around 35-45 dB indoors. The calculated safe distance from a 110 dB source to reach 85 dB should be approximately 5-6 meters in theory, though indoor conditions may alter this value.

Scientific questions:

- Why does the inverse square law predict a 6 dB decrease for each doubling of distance?
- In what conditions might the measured decrease be less than 6 dB per doubling? More than 6 dB?
- How long can a person safely be exposed to 85 dB? To 100 dB? To 110 dB?
- Why is white noise used instead of a pure tone for this experiment?
- How do concert venues manage sound levels to protect audience hearing while maintaining the experience?
- What is the difference between sound intensity (W/m²) and sound level (dB)?

Scientific explanations:

The propagation of sound in air follows the inverse square law: sound intensity decreases proportionally to the square of the distance from the source. This relationship is explained by the spherical dispersion of sound energy from the point emitting source.

For an omnidirectional source, the power P is distributed over the surface of a sphere of radius r, therefore the intensity I = P/(4πr²). However, we perceive and measure sound according to the logarithmic decibel scale: L = 10log(I/I₀).

Therefore, when the distance triples, the intensity is divided by 9 (3²), which corresponds to a reduction of approximately 9.5 dB. This difference is significant since an increase of 10 dB is perceived as a doubling of sound volume.

The hearing risk level starts from 85 dB for prolonged exposure, and every 3 dB increase doubles the sound power. In a concert, levels can reach 100-110 dB near the speakers, well beyond the pain threshold (120 dB).

Using the smartphone microphone with FizziQ provides reliable relative loudness measurements, although absolute values may vary slightly between models.

Extension activities:

Frequently asked questions:

Q: The sound level does not decrease by 6 dB when I double the distance. Why?
R: The 6 dB rule applies to a point source in free space (no reflections). Indoors, sound reflected from walls, floor, and ceiling adds to the direct sound, reducing the apparent drop. Try the experiment in a larger space or outdoors for closer agreement with theory.

Q: The readings fluctuate a lot at large distances. Is the data still usable?
R: At large distances, the source signal approaches the background noise level, causing fluctuations. Take longer recordings (20-30 seconds) and use the average value. If the background noise is within 10 dB of the signal, the measurement is significantly affected.

Q: Why do you recommend white noise rather than music or a pure tone?
R: White noise contains all frequencies at equal intensity, providing a consistent broadband signal that averages out frequency-dependent effects like standing waves and directional radiation patterns.

Q: How accurate is the smartphone microphone for measuring sound levels?
R: Smartphone microphones are reasonably accurate (±2-3 dB) for relative measurements, which is sufficient for verifying the inverse square relationship. Absolute calibration varies between devices, so comparing levels between two different phones may introduce systematic errors.