What is SPL (Sound Pressure Level)? – Definition & Examples

Jan 10, 2020 | Sound

The pressure within a sound wave determines the loudness of the sound. In this lesson, learn how to calculate the sound pressure level of a sound wave and what this measurement represents.

What Is Sound Pressure?

When it comes down to it, your ears are pretty amazing. They allow you to hear sounds as quiet as a whisper and as loud as a jet engine. How exactly do sound waves get transmitted to your ears so that you can hear?

It starts with a vibration in the air. A whisper only vibrates the air a little bit, while a jet engine vibrates it A LOT. This vibration creates a pressure wave that passes through the air, spreading out in all directions as it goes. Sound pressure is the pressure measured within the wave relative to the surrounding air pressure. Loud sounds produce sound waves with relatively large sound pressures, while quiet sounds produce sound waves with relatively small sound pressures.

Sound pressure, like other kinds of pressure, is commonly measured in units of Pascals (Pa). The quietest sound that most people can hear has a sound pressure of 2 x 10-5 Pa, so this pressure is called the threshold of human hearing.

If your ear happens to be in the path of the sound wave, the vibrating air molecules hit your eardrum and cause it to start vibrating too. When your eardrum starts vibrating, it bumps into the tiny bones in your middle ear and makes them vibrate. The vibration passes all the way into your inner ear where the vibration of tiny hair cells sends signals to your brain, thus letting you hear the sound. The pressure of the sound wave corresponds to how loudly you hear the sound. As the sound pressure increases, the pressure on your eardrum increases as well, making the sound seem louder to you.

What Is Sound Pressure Level?

Because your ears are sensitive to a very wide range of sound pressure, it makes sense to use a logarithmic scale to measure the loudness of a sound. Sound pressure level uses a logarithmic scale to represent the sound pressure of a sound relative to a reference pressure. The reference sound pressure is typically the threshold of human hearing: remember that it’s 2 x 10-5 Pa.

Sound pressure level is measured in units of decibels (dB) and is calculated using the following equation, where p is the sound pressure of the sound wave and po is the reference sound pressure:

 

Calculating Sound Pressure Level

Let’s use this equation to calculate the sound pressure level of a jet engine if you’re standing one meter away from it. At this distance, the sound pressure would be about 600 Pa.

First, remember that the reference pressure is 2×10-5 Pa and divide the sound pressure of the jet engine by this reference pressure. Calculating this, we get:

This is a very loud sound with a sound pressure level of 150 dB!

How does this compare to the sound pressure level of a quieter sound, like a television in your living room? This type of sound would have a sound pressure of about 2 x 10-2 Pa. We can calculate this like before, with our sound pressure formula. We get: 

So, when you’re watching television, you’re hearing sounds with a sound pressure level of about 60 dB.

Because the sound pressure level is measured using a logarithmic scale, small changes in sound pressure level correspond to large changes in the loudness of the sound. Even though the sound pressure level of the jet engine (150 dB) is only two and a half times bigger than the sound level of your television (60 dB), the jet engine is actually 30,000 times louder!

You can see how this works being reflected in the table right now:

 

Lesson Summary

Sound pressure is the pressure measured within a sound wave relative to the surrounding air pressure. Loud sounds produce sound waves with relatively large sound pressures, while quiet sounds produce sound waves with relatively small sound pressures.

Sound pressure level uses a logarithmic scale to represent the sound pressure of a sound relative to a reference pressure, and it’s measured in units of decibels (dB). The sound pressure level at the threshold of human hearing is actually 0 dB, which has the same pressure as the reference pressure, 2 x 10-5 Pa.

The formula for finding the sound pressure level is:

 

 

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