Decibels and dB SPL

(Note: This is a slightly modified excerpt of Chapter 1 from a book I’ve been working on entitled “Digital Audio for C++ Programmers.”)

The decibel is perhaps one of the most confusing and misunderstood topics in audio. It has a confusing formula that appears to change based on the context. It’s also used in a variety of applications beyond audio. In fact, much of the documentation you’ll find is actually related electronics and telecommunications. And to muddy things even more, by itself the plain ole decibel doesn’t even really convey much meaning. It merely relates one power value to another. So, if after reading this article, you still find decibels confusing, don’t fret. You’re in good company.

The decibel originated with telephony in the early 1900’s. It was used as a way to describe the power efficiency of phone and telegraph transmission systems. It was formally defined as 1/10th of something called a bel. Interestingly, the bel was rarely used. The decibel got all the glory. The decibel has since found its way into all sorts of other domains, such as optics, electronics, digital imaging, and, most importantly to me, audio.

There are two benefits to using the decibel. The first is that switching to a logarithmic scale converts an awkward range of values (e.g., 0.0002 Pascals – 20 Pascals) to something much easier to reason about (e.g., 0 dB SPL – 120 dB SPL) . The other benefit applies to audio – a logarithmic scale is much closer to how the human ear actually hears. With a linear scale, like Pascals, doubling the value doesn’t usually feel like a doubling of loudness. With decibels, we actually get a scale that’s much closer to how to perceive loudness.

The decibel, in the generic sense, is not strictly a physical unit. When we think of physical units, we typically think about things like Amperes (number of moving electrons over time), Pascals (pressure), meters (distance), Celsius (temperature), etc. These are absolute units that correspond to physical things. The decibel isn’t like that. It’s a relative unit. It provides a relation of two things, which are themselves physical units. And it does this on a logarithmic scale.

The general formula for the decibel is as follows.

The decibel, abbreviated dB, is the logarithmic ratio between two power values. One of these two values is a reference value. The other is a measured value.

You may notice the phrase “power value” in that formula. In physics, this means the amount of energy transferred over time. The unit for power is usually the watt. However, there are plenty of units used that aren’t power values (such as Pascals in acoustic audio). So we have to convert those units into something related to power. This typically just means squaring the measured and reference values. The decibel formula ends up looking like so.

With logarithms, we can pull that exponent out and turn it into a multiplication.

This can be simplified even further like so.

And this is the formula you’ll most likely encounter when applying the decibel to measured and reference units which aren’t power-based (like Pascals in acoustic audio). It’s just a derivation of the original formula with the measured and reference values tweaked.

Standard Reference Values

A lot of domains, such as electronics and audio, have standardized reference values for the various things being measured. When we talk about these standardized flavors of the decibel, we add suffixes to the dB abbreviation. Examples of this are dBV (voltage based), dBm (radio power), dBZ (radar power), etc. The one we’re most concerned with in the field of acoustic audio is dB SPL.

dB SPL

dB SPL is the most common flavor of decibel for indicating the loudness of acoustic audio. SPL stands for sound pressure level. The reference value used in calculating dB SPL is the threshold of human hearing – 0.000020 Pa. We plug this into the decibel formula along with a measured value, also in Pascals, to come up with a dB SPL value.

A measurement of 0 dB SPL is considered the threshold of human hearing. That is, it’s the quietest sound that the human ear is capable of hearing. On the upper end of the scale, somewhere between 130 dB SPL and 140 dB SPL, is what’s referred to as the threshold of pain. When the volume of sound approaches this level, it can result in physical discomfort and some amount of hearing loss is almost certain.

The following two tables shows some common sounds and their approximate sound pressure measurements. The first table shows measurements in Pascals. The second table shows them in dB SPL. Compare them and you’ll see that dB SPL is much less awkward to use.

Sound SourceDistance from EarPascals
Jet Engine1 meter632
Threshold of PainAt ear20 – 200
Yelling Human Voice1 inch110
Instantaneous Hearing Loss Can OccurAt ear20
Jet Engine100 meters6.32 – 200
Chainsaw1 meter6.32
Traffic on a Busy Road10 meters0.2 – 0.63
Hearing Loss from Prolonged ExposureAt ear0.36
Typical Passenger Car10 meters0.02 – 0.2
Television (typical volume)1 meter0.02
Normal Conversation1 meter0.002 – 0.02
Calm RoomAmbient0.0002 – 0.0006
Leaf rustlingAmbient0.00006
Threshold of HearingAt ear0.00002
Sound Pressure Measured in Pascals, “Sound pressure” Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc, 22 July 2004, https://en.wikipedia.org/w/index.php?title=Sound_pressure&oldid=1112496481. Accessed 29 Nov. 2022.

Sound SourceDistance from EardB SPL
Jet Engine1 meter150
Threshold of PainAt ear130-140
Yelling Human Voice1 inch135
Instantaneous Hearing Loss Can OccurAt ear120
Jet Engine100 meters110-140
Chainsaw1 meter110
Traffic on a Busy Road10 meters80-90
Hearing Loss from Prolonged ExposureAt ear85
Typical Passenger Car10 meters60-80
Television (typical volume)1 meter60
Normal Conversation1 meter40-60
Calm RoomAmbient20-30
Leaf rustlingAmbient10
Threshold of HearingAt ear0
Sound Pressure Measured in dB SPL, “Sound pressure” Wikipedia: The Free Encyclopedia. Wikimedia Foundation, Inc, 22 July 2004, https://en.wikipedia.org/w/index.php?title=Sound_pressure&oldid=1112496481. Accessed 29 Nov. 2022.

There are instruments available that measure sound pressure levels and report dB SPL. One such instrument is shown below. This happens to be my personal db SPL meter.

These devices are fun to take to concerts or demolition derbys if for no other reason than giving you the intellectual authority to complain about permanantly damaged hearing.

Conclusion

Hopefully, this article has helped demystify the decibel. Mathematically, they’re not something to be feared. It’s usually the logarithms that scare folks away. And if you’ve long since forgotten how logarithms work, go brush up on them and come back to this article a second time. It will make a lot more sense.

If you found this content useful, or if something could have been explained better, please leave me a comment below.

Until next time.

Digital Audio with the DFPlayer

My oldest daughter and I recently built one of Mr. Baddeley’s Baby R2s. These units are small, almost cartoonish, radio-controlled R2D2s that are extremely easy to build. And fun! But something missing from the design (at least at the time of this writing) is the ability for these little guys to produce sounds. And what’s an R2D2 with his signature beeps and boops?

For my life-size R2, I incorporated an MP3 Trigger from Sparkfun and paired that with an Arduino. But I couldn’t use that here because the MP3 Trigger is too large. The Baby R2s just can’t accommodate it. So I went in search of something else. And that’s when I came across the DFPlayer from DFRobot.

In this article (the first of three), we’ll be exploring the DFPlayer and beginning our journey into ultimately using an RC radio to trigger audio. If that’s not something that interests you, no worries. This article is focused entirely on the DFPlayer.

DFPlayer

DFRobot’s DFPlayer is a tiny (~ 21mm x 21mm) module that’s capable of playing MP3, WMV, and WAV audio data. It features a micro-SD slot for your audio files. It can be connected directly to a small speaker (< 3 W) or an amplifier. And it can be controlled a few different ways, including via a serial connection which works well for my particular needs.

Perhaps the biggest selling point for the DFPlayer is its price – $6 as of this writing. Compare that to the SparkFun MP3 Trigger, which comes in at around $50. The DFPlayer is practically a guilt-free impulse buy. In fact, I picked up a 3 pack from Amazon for around $10.

One of the downsides to this module is that there are various models that exhibit different tolerances to electrical noise, which means you might struggle with an audible hiss. Killzone_kid posted a great writeup on the Arduino forums that examines some of the models and makes some recommendations on possible ways to mitigate the hiss. Some of the flavors also apparently have compatibility issues with the officially supported DFPlayer Arduino library, which we’ll look at in a bit.

Here’s the pin diagram for the DFPlayer.

Left-Side Pins

There’s a Vcc pin and a ground pin as you might expect. These pins are used to power up the device. The source voltage must be between 3.2V and 5V.

The Serial RX and TX pins are used to provide a serial interface for controlling the device. It defaults to 9600 baud, 1 data bit, no check bits, no flow control. The serial protocol is detailed in the datasheet. But there’s also an official support library for Arduino called DFRobotDFPlayerMini that implements the serial protocol and provides a high-level interface for controlling the DFPlayer.

The Amp Out pins are for connecting to an audio amplifier or headphones.

The Spkr pins are for very small speakers – less than 3 watts. This is actually what I’ll be using for my project. I’m connecting the DFPlayer to a small speaker that I harvested from one of my kids’ annoying…er, I mean, broken toys.

 

Right-Side Pins

On the right-hand side of the pin diagram, you’ll see pairs of pins for I/O and ADKey. These are two other mechanisms for controlling the DFPlayer. We’ll use the I/O pins to test the DFPlayer shortly. But we won’t be using the ADKey pins at all. I won’t be discussing them further. If you want to learn more about them, I advise you to check out the DFPlayer Wiki.

The USB pins allow the DFPlayer to work as a USB device. I haven’t been able to find very much information about this. It’s not discussed much in the DFPlayer manual. Apparently, it provides a mechanism for updating the contents of the SD card from your PC. This could be handy for projects where the DFPlayer ends up hidden away inside of an enclosure that can accommodate a USB connector on the outside. For my project, I don’t need it so I won’t be exploring it. However, if anyone knows where I can find more information about this, please let me know. It could come in handy on another project.

The pin labeled “Playing Status”, referred to as the “Busy” pin, is normally high when the device is idle and goes low when the device is playing audio. The device already has a small LED that lights up when it’s playing files. But if that’s not good enough, you can connect an LED to this pin, or connect it to a microcontroller for more sophisticated behaviors.

Adding Media Files

The DFPlayer manual describes the naming of folders and files on the SD card. With regards to files, it specifies names using 3 digit numbers, such as 001.mp3, 002.wav, etc. Folders can be named similarly. I didn’t actually create any folders on my SD card, and it worked just fine. My file layout looks like so.

Testing the DFPlayer

Before doing anything else, I like to do a quick smoke test. This simply involves powering up devices straight out of the box (if feasible) and seeing if any magic blue smoke appears. I also like to note if any LEDs light up, as there’s often a power LED that will indicate the device is at least turning on. In this case, nothing happened. After a bit of reading, I learned that the device’s single LED only lights up when it’s actually playing media. So at this point, I wasn’t sure if it was even powering up. My benchtop power supply said the DFPlayer was pulling a small amount of current, so something was happening.

Next, I wanted to see if I could get some sound out of the device. I plugged in my micro SD card and connected my speaker. The I/O pins (9 and 11) were the key to this. Grounding I/O pin 1 for a quick duration will cause the DFPlayer to play the “next” track. Grounding it for a long duration lowers the audio level. Grounding I/O pin 2 for a quick duration will cause the DFPlayer to play the “previous” track. Grounding it for a long duration raises the audio level.

I grounded I/O pin 2 for a couple of seconds to get the audio level all the way up and then quickly grounded I/O pin 1 with a quick tap. The device’s LED lit up and I immediately heard some beeps and boops. The device was working. Success!

Now I knew any issues I might have trying to drive it over a serial connection would be limited to my code and/or the serial interface itself.

Connecting the Arduino

For this project, I used a Nano clone from Lavfin. These come with the pins pre-soldered. When I originally bought this, you could get a pack of 3 from Amazon for around $14. The price has since gone up to $28 as of this writing (presumably, because of supply chain issues).

For testing, I’m used a Nano expansion board. This provides convenient screw terminals.

 

I connected the DFPlayer to the Arduino using the serial pins of the DFPlayer and digital pins 10 and 11 of the Arduino. The DFPlayer’s RX pin connects to the Arduino’s digital pin 11. The DFPlayer TX pin connects to the Arduino’s digital pin 10.

Why didn’t I use the Arduino’s serial pins? I could have. But the process of writing new code to the Arduino makes use of the UART. So I’d have to disconnect and reconnect the DFPlayer every time I wanted to update the software.

I don’t recommend connecting the DFPlayer Vcc and ground pins to the Arduino’s 5v and ground pins unless you REALLY need to leverage the Arduino’s voltage regulator. This is how I’ve seen it wired in the online examples. It’s convenient, sure. But the Arduino has current supply limitations. Having the DFPlayer and the Arduino connected independently to the power source is the better option.

This is how my DFPlayer and Nano are wired together.

The source code for my Arduino/DFPlayer test is as follows.

#include "Arduino.h"
#include "DFRobotDFPlayerMini.h"
#include "SoftwareSerial.h"
 
static SoftwareSerial g_serial(10, 11);
static DFRobotDFPlayerMini g_dfPlayer;
 
/**
 * Called when the Arduino starts up.
 */
void setup()
{
    // We'll use the built-in LED to indicate a communications
    // problem with the DFPlayer.
    pinMode(LED_BUILTIN, OUTPUT);
    digitalWrite(LED_BUILTIN, LOW);
 
    // Let's give the DFPlayer some time to startup.
    delay(2000);
 
    g_serial.begin(9600);
 
    if (!g_dfPlayer.begin(g_serial))
    {
        // There's a problem talking to the DFPlayer. Let's turn on the LED
        // and halt.
        digitalWrite(LED_BUILTIN, HIGH);
        while(true)
        {
            delay(0);
        }
    }
 
    // Valid values for volume go from 0-30.
    g_dfPlayer.volume(20);
    // Plays the first file found on the filesystem.
    g_dfPlayer.play(1);
}
 
// Called over and over as long as the Arduino is powered up.
void loop()
{
    static unsigned long timeLastSoundPlayed = millis();
 
    // We're going to iterate through the sounds using DFRobotDFPlayerMini's next() function,
    // playing a new sound every five seconds.
    if ((millis() - timeLastSoundPlayed) &gt; 5000)
    {
        g_dfPlayer.next();
        timeLastSoundPlayed = millis();
    }
 
    // Consumes any data that might be waiting for us from the DFPlayer.
    // We don't do anything with it. We could check it and report an error via the
    // LED. But we can't really dig ourselves out of a bad spot, so I opted to
    // just ignore it.
    if (g_dfPlayer.available())
        g_dfPlayer.read();
}

To build this sketch, the DFRobotDFPlayerMini library must be installed. This can be downloaded from GitHub –
https://github.com/DFRobot/DFRobotDFPlayerMini. Installing it is as simple as extracting it to the Arduino libraries directory (e.g., C:\Program Files (x86)\Arduino\libraries).

Line #5 creates an instance of the SoftwareSerial class. I call it g_serial. This is used to emulate a UART over digital pins. I reserved the hardware UART so I could update the software on the Arduino while being connected to DFPlayer. If you’d rather use the hardware UART and the Serial global variable, that’ll work fine too. You just have to disconnect the DFPlayer every time you need to update the code. The two arguments to the SoftwareSerial constructor are the pin numbers for RX and TX, respectively.

Line #2 of the source above includes the DFRobotDFPlayerMini header file, which brings the various DFRobotDFPlayerMini types into scope. I then declare the static global instance of DFRobotDFPlayerMini called  g_dfPlayer. This will be the object we use to interact with the DFPlayer.

The first thing the setup() function does is configure the Arduino’s on-board LED. Since I’m not actually using the Serial Monitor in the IDE, I wanted to light this up if there were problems initiating communications with the DFPlayer.

I then delay execution for 2 seconds to give the DFPlayer time to startup. This is important to note because I didn’t see this happen in any of the sample sketches that cames with the DFRobotDFPlayerMini library. Without the delay, things just wouldn’t work for me. I don’t know if it’s because of my particular flavor of DFPlayer and/or Arduino. But 2 seconds seems to be the delay I need to get the devices to talk to one another.

I call begin() on g_serial with an argument of 9600 baud since this is the baud rate supported by DFPlayer. I then attempt to start communication with the DFPlayer by calling g_dfPlayer’s begin() function, passing it the serial object I want it to use. If an error occurs, I light up the LED and effectively halt. If no error occurs, I crank the volume up to 20 (out of 30 max) and play the first file on the DFPlayer’s file system. If all things are well, I should hear a sound.

In the loop() function, we do two things – 1) check to see if it’s been 5 seconds since we last played a sound and, if so, play one and 2) eat up any data sent to us by the DFPlayer. I should point out that I don’t actually know if we need to consume data if we’re not doing anything with it. But without diving too deep into the DFRobotDFPlayerMini code, I’m erring on the side of caution and hoping to keep some buffer somewhere from filling up.

Once this code was compiled and flashed to the Arduino, I had to restart both the Arduino and the DFPlayer. After a couple of seconds, I started hearing more beeps and boops.

Wrapping Up

This code is a good starting point. I encourage you to explore the sample code that accompanies the DFRobotDFPlayerMini library. There are some good nuggets there.

In the next article, I’ll be focusing on interfacing a radio controller with the Arduino. And then a third article will follow that which will tie everything together so that we can trigger our audio with a radio.

Until next time…

Appendix B – Introduction to Windows Core Audio

For a little while now, I’ve been hard at work on a little side project. I almost hesitate to announce it at this point, because it’s still very early. But, what the heck. Why not. I’ve started writing a book. And no, it’s not one full of suspense and intrigue. Nor is it the next young adult break-out series. Turns out, I’m writing a programming book. The working title is “Practical Digital Audio for C++ Programmers”, which I admit is a mouthful. Henceforth (at least as far as this blog entry is concerned), I shall refer to it as PDA4CPP.

When I first started my audio programming journey, I quickly discovered there was a huge hole in the information available to newcomers to the field. There was plenty of material to be found regarding specific audio libraries. And there was even more material that discussed, in very mind-bendy ways, things like audio effects and synthesis that assumed you already had some level of comfort with digital audio programming. But there was very little in-between. And as a complete newb, I found it super discouraging. So I decided to do something about it. PDA4CPP is the fruits of my labor.

As I mentioned, the book is in its infancy. Only one chapter has been completed to date – Appendix B: Introduction to Windows Core Audio. But it’s a beast, coming in at 170 pages. In it, I talk about where Core Audio fits into the Windows story, the Windows audio architecture, device discovery, audio formats, WASAPI, audio rendering, and audio capturing.

Why did I start with Appendix B? Some of it was because of the questions and feedback I received from my blog entry, “A Brief History of Windows Audio APIs”. But mostly, I started with Appendix B because that’s where I needed to. Most of the book’s code will be implemented around a custom audio library that’s effectively a thin wrapper around platform-specific audio code. The Windows side of things provided as great a starting point as any.

Something I’m going to experiment with is making drafts of the book’s chapters available for purchase as I complete them. Not only will this help motivate me to keep writing, but it will also help me gauge interest. Appendix B is the first chapter available for purchase. Pricing for each chapter will vary based on each chapter’s size and density. More information can be found on the book’s page, which can be found under the “Pages” menu. An excerpt is available, as well as the chapter’s source code.

If you purchase the chapter and love it, hate it, or have ideas on how to improve it, please email me or leave a comment below.

Thanks!

-Shane