The Memory Trick
💡 Every 10 dB = 10× the Intensity
Sound intensity is measured on the decibel (dB) scale, which is logarithmic rather than linear. This means the scale doesn't increase in simple equal steps — every increase of 10 dB represents a full 10-fold increase in actual sound intensity, not just a 10% increase.
Why It Works
Human hearing itself is roughly logarithmic in how it perceives loudness — our ears can handle an enormous range of actual sound intensities (from a whisper to a jet engine), and a logarithmic scale compresses that huge range into manageable numbers, at the cost of each unit representing a multiplicative, not additive, change.
Step by Step
Working With the Decibel Scale
1
Know the key reference points
0 dB marks the threshold of human hearing (the quietest audible sound). 60 dB is roughly normal conversation. 120 dB is the threshold of pain.
A whisper might register around 30 dB, while a rock concert can reach 110-120 dB — a difference the linear number doesn't fully convey without understanding the logarithmic scale.
2
Every 10 dB is a 10× multiplier
This compounds quickly — a 20 dB increase means 10×10 = 100× more intense; a 30 dB increase means 1000× more intense.
A sound at 80 dB is 10× as intense as one at 70 dB, and 100× as intense as one at 60 dB.
3
Perceived loudness is a separate, related scale
Perceived loudness (how much louder something SOUNDS to a human) roughly doubles for every 10 dB increase — a related but distinct concept from the actual physical intensity multiplier.
A sound at 70 dB is roughly perceived as twice as loud as one at 60 dB, even though the actual physical intensity increased by a factor of 10, not 2.
🏥 Worked Example
A vacuum cleaner produces 70 dB of sound. A jet engine at close range produces 140 dB. How many times more intense is the jet engine's sound compared to the vacuum cleaner's?
1
Find the difference in decibels: 140 − 70 = 70 dB difference.
2
Convert to intensity multiplier: since every 10 dB is a factor of 10, a 70 dB difference means 7 factors of 10: 10⁷ = 10,000,000.
3
Conclusion: the jet engine's sound is 10 million times more intense than the vacuum cleaner's — a striking illustration of how quickly the decibel scale compounds.
📌 Exam Application
Exams test correctly converting a decibel difference into an actual intensity ratio (using powers of 10 per 10 dB), and distinguishing physical intensity multiplication from perceived loudness doubling.
⚠️ Most Common Sound Intensity and Decibels Mistakes
The most common trap is treating decibels as a linear scale — assuming 20 dB is simply 'twice as loud' as 10 dB. In reality, 20 dB represents 100 times the actual sound intensity of 10 dB, since each 10 dB step is a multiplicative, not additive, factor of 10.
✓ Quick Self-Test
1) What does the decibel scale represent — linear or logarithmic increases in intensity? Logarithmic. 2) How much more intense is a sound at a 10 dB increase compared to the original? 10 times more intense. 3) How much more intense is a sound at a 20 dB increase compared to the original? 100 times more intense (10 × 10). 4) What are the approximate dB levels for the threshold of hearing, normal conversation, and the threshold of pain? 0 dB, 60 dB, and 120 dB respectively. 5) By roughly what factor does PERCEIVED loudness (not actual intensity) increase for every 10 dB? It roughly doubles.
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