How loud is 20 dB compared to 10 dB?

Have you ever wondered what the numbers on a sound level meter actually mean? You might assume that a 20 decibel (dB) sound is simply twice as loud as a 10 dB sound. It seems logical, but the way we measure sound is more complex than that. The relationship isn't a simple straight line.

Understanding the decibel scale is key to appreciating the true difference between these values. It's not just about numbers; it's about grasping how sound energy works and how our ears perceive it. This guide will walk you through the fundamentals of decibels, explain the difference between sound intensity and perceived loudness, and show you why a 20 dB sound is significantly more powerful than you might think. By the end, you'll have a clear understanding of what those decibel ratings really represent.

What are Decibels (dB)?

A decibel (dB) is the standard unit used to measure the intensity of a sound, also known as its amplitude or volume. Sound is essentially energy that travels in waves, and decibels provide a way to quantify the pressure or forcefulness of these waves. The more amplitude a sound has, the higher its decibel level.

Crucially, the decibel scale is not linear like a ruler. Instead, it is a logarithmic scale. This means it increases exponentially, allowing it to cover the vast range of sounds the human ear can detect, from the faintest whisper to the roar of a jet engine. A logarithmic scale is a way of measuring something that changes rapidly. Instead of each step on the scale being an equal addition (like 1, 2, 3, 4), each step is a multiplication.

This logarithmic nature is why a small increase in decibels can represent a massive jump in sound intensity.

Understanding the Logarithmic dB Scale

Because the decibel scale is logarithmic, every increase of 10 dB represents a tenfold increase in sound pressure level, which is a measure of sound intensity.

Let's break that down:

• A sound at 10 dB is 10 times more intense than a sound at 0 dB (which is near total silence).
• A sound at 20 dB is 10 times more intense than a sound at 10 dB.
• This means a sound at 20 dB is actually 100 times more intense than a sound at 0 dB.

This exponential growth continues up the scale. A 30 dB sound is 1,000 times more intense than 0 dB, and a 40 dB sound is 10,000 times more intense. This is a crucial concept to grasp when comparing decibel levels.

To put this into context, here are the decibel levels of some common sounds:

• A quiet whisper: 30 dB
• Normal conversation: 60 dB
• Heavy city traffic: 85 dB
• Lawnmower: 90 dB
• Live rock concert: 120 dB
• Siren from an emergency vehicle: 120 dB
• Fireworks: 140-160 dB

As you can see, the jump from normal conversation (60 dB) to heavy traffic (85 dB) might seem small numerically, but the sound intensity is vastly different.

Intensity vs. Loudness: What's the Difference?

While sound intensity increases tenfold with every 10 dB, our perception of loudness does not. The terms "intensity" and "loudness" are often used interchangeably, but they refer to two different things.

• Intensity is a physical, objective measurement of sound energy. It refers to the actual acoustic energy passing through a certain area per second.
• Loudness is a subjective, psychological perception of that sound energy. It's how our brain interprets the intensity of a sound.

Our ears are also logarithmic in how they perceive sound. As a general rule of thumb, an increase of 10 dB is perceived by the human ear as being roughly twice as loud. So, while a 20 dB sound is ten times more intense than a 10 dB sound, it will sound about twice as loud to a person, which is why an earplug with a high decibel reduction rating is so important for protecting your hearing.

This is an important distinction. The physical energy of the sound wave increases much more dramatically than our brain's interpretation of it. This logarithmic response of our hearing allows us to handle an incredible range of sound levels, from a pin dropping to a thunderclap, without being overwhelmed.

The Maths Behind the Decibels

For those who are interested in the specific formula, the decibel level (L) of a sound is calculated using the following equation:

L = 10 · log₁₀(I / I₀)

Here's what each part means:

• L is the decibel level.
• log₁₀ is the base-10 logarithm.
• I is the intensity of the sound being measured.
• I₀ is the reference intensity, which is the quietest sound the average human ear can detect (approximately 10⁻¹² watts per square meter).

Using this formula, let's see why a 20 dB sound is ten times more intense than a 10 dB sound.

For a 10 dB sound:
10 = 10 · log₁₀(I₁ / I₀)
1 = log₁₀(I₁ / I₀)
10¹ = I₁ / I₀
I₁ = 10 · I₀

For a 20 dB sound:
20 = 10 · log₁₀(I₂ / I₀)
2 = log₁₀(I₂ / I₀)
10² = I₂ / I₀
I₂ = 100 · I₀

As you can see, the intensity of the 20 dB sound (I₂) is 100 times the reference intensity, while the intensity of the 10 dB sound (I₁) is only 10 times the reference intensity. Therefore, the 20 dB sound is ten times more intense than the 10 dB sound (100 / 10 = 10).

What This Means in the Real World

Understanding the power of the decibel scale is essential for protecting your hearing. Because the scale is logarithmic, even seemingly small increases in decibels can expose you to significantly more sound energy, which can lead to noise-induced hearing loss (NIHL).

According to the National Institute on Deafness and Other Communication Disorders (NIDCD), prolonged exposure to any noise at or above 85 dB can cause gradual hearing loss. This is the level of heavy city traffic or a noisy restaurant.

Consider these safety guidelines:

• 85 dB (Lawnmower): Damage can occur after about 8 hours of exposure.
• 100 dB (Motorcycle): Damage can occur after just 15 minutes.
• 110 dB (Rock Concert): Damage can occur in less than 5 minutes.
• 120 dB (Siren): Immediate danger to hearing.

This is why wearing hearing protection, like earplugs or earmuffs, is so important when you're in loud environments. A small reduction in decibels can mean a massive reduction in the sound intensity reaching your ears, safeguarding your hearing for years to come.

A Clearer Understanding of Sound

To summarise, a 20 dB sound is not simply twice as loud as a 10 dB sound. In terms of physical energy, it is ten times more intense. However, due to the logarithmic nature of human hearing, we perceive this tenfold increase in intensity as a sound that is roughly twice as loud.

Grasping the difference between intensity and perceived loudness, and understanding that the decibel scale is logarithmic, is key. It helps you appreciate the true power of sound and highlights the importance of protecting your hearing from levels that might seem only slightly higher but are, in reality, exponentially more powerful.