Babies cry. Sometimes they cry a LOT. And loudly. As a new mom, my baby’s cry was a horrible sound that made me upset and sick to my stomach and not being able to stop it was (and still is) the worst feeling in the world (at least it feels that way in a hormonal, sleep-deprived state). There’s a good physical reason for this, but more on that some other time. Today I want to talk about volume.
It seemed that our daughter cried louder than other babies. ‘Everyone’ told us that newborns do not cry loudly and that it just seemed that way to us as parents. Then friends and family started commenting on “what an extraordinarily healthy set of lungs she has!” Being the scientifically minded folk that we are, my husband and I decided to measure the volume of her cries.
At about two months old, we measured our daughter’s cry to be 122 dB at about 4″ from her mouth.
Okay, what does that actually mean? What is a dB and how loud is 122 of them and why did I feel the need to include the distance?
The sounds that we hear are waves of energy that travel through the air by changing the air pressure by small amounts. This vibration of the air vibrates our ear drums and causes us to hear a sound. For more on how hearing works, there is an interesting article on this at the How Stuff Works website: How Hearing Works.
Today I’m interested in how we measure sounds. Normally, we would measure how much energy reaches the area of our ear in a certain amount of time, or the intensity of the sound, which is usually measured in Watts/(meter)2. To give you an idea of some common intensity values, the threshold of hearing (smallest sound we can hear) is 1 x 10-12 W/m2 and the threshold of pain is 1 W/m2. That means that we feel pain at an intensity level that is 1012 times larger than the smallest sound we can hear – that’s a trillion (a million million) times larger. But of course, sounds that hurt my ears don’t sound a trillion times louder than the faintest whispers. Why not?
Interestingly, our ears do not work on a linear scale – that is to say that if twice as much energy hits our ear in a given time, it does not sound twice as loud to us. Our ears interpret sounds logarithmically, so we have a unit of measurement that describes how loud a sound is, or the sound level. This is measured in decibels, or dB for short. For those of you who like equations, the formal definition of sound level for a given intensity is
For those of you who don’t like equations, this table might be more useful in understanding what different values of intensity and sound level mean to you.
Okay, so what does that mean about my daughter? Her loudest screams are above the pain threshold. Ow! The Occupational Safety & Health Administration (OSHA) recommends that that you not be exposed to that level of noise at all in the workplace. Too bad my daughter does not abide by their recommendations. It really does hurt my ears when she screams and I am holding her.
There is one more piece to this loudness puzzle, though. I mentioned that we measured her scream at 4” from her mouth. Why does this matter? Sound spreads out in all directions as it travels away from my daughter’s mouth, so the energy gets spread out over a sphere (approximately) as it travels away from her mouth (see silly cartoon at right). The farther away you get, the lower the intensity (and sound level) of the cry. Good news for everyone else, not such good news for me holding my daughter on my shoulder so that her mouth is only a couple of inches away from my ear. To better see how the sound level decreases with distance, a graph of sound level vs. distance for her cry is below:
Does this have an effect on the theory that parents think their children are louder? Is it just that the parent’s are so much closer? Probably not. We are conditioned as parent’s to hear and respond to our children’s cries because they need us.
Then what does this all mean, other than being a good example for sound level problems for my introductory Physics students? Not much, I suppose. If my daughter is screaming at full volume, I should be wearing earplugs, but if she’s screaming that loud for an extended period of time, I’m going to be less worried about my ears than about what is wrong with her to make her scream so loud. Fortunately, she doesn’t scream like that often anymore. It does mean that you can ignore all those people who tell you that your child only sounds loud to you. Tell them that some babies scream above the pain threshold.
If you’re curious about you baby’s cry (or other sound levels), my husband and I used a dedicated sound meter, which most normal people don’t own, but, as with everything these days, there is an App for this! Several in fact. With a small financial (~$1) and time commitment, you too could measure your baby’s screams!