Loudness and sound pressure levels

This morning the blogs and twitter feeds were linking all over the place to a passive amplifier for your iPhone. (See it here: Science & Sons OS v1.0)

The idea behind a passive amplifier is that it requires no electrical power to increase the amplitude of the sound wave which is presented to your ear. Just pop your iphone into the cradle and crank up the tunes. As long as the battery in the iphone is charged, you have amplified sound.

It sounded cool, so I checked it out. This is what caught my eye:

The Phonofone III is an elegantly designed passive amplifier crafted from ceramic and designed explicitly for iPhone. This clever device amplifies the volume emited from an iPhone internal speaker roughly 4x (approx. 60 decibels).

Wait. What? I get a 60 dB gain out of a device with no power?  Let's see if that passes the sanity check. I don't have an iphone, but I have heard the iphone playing audio from its internal speaker. Unamplified, at a moderate level, I would say the sound level observed from an ipod (at an average distance) is about the same as the sound level of a typical conversation.  Let's look at what the approximate sound level would be:

(I found this chart on OSHA's website. I assume the image is public domain, like most government images.)  From the chart you can see that conversation at 1 m is approximately 60 dB(A).  (The "A" means A-weighted, which is a weighting factor used to approximate the frequency response of the human ear.)   Let's be conservative and estimate the iphone unamplified level to be about 55 dB. That means that if I drop the iphone into the passive device the sound level should be 55 dB + 60 dB = 115 dB.  That's louder than the "Discotheque" rating in the chart (when/where was this chart generated?) which is also about 20 dB louder than a jackhammer at 15 meters.  Somehow I really doubt that the single horn + iphone is going to be able to compete with the speakers and amplifier of a dance club.

What about the other claim?  They say the sound will be about 4x louder.  Here's where the claim might hold some water. The basic idea of a horn is to provide better impedance matching  between the driver and the sound field and to control directivity of the sound radiation.  Assuming the horn is pointing at an observer, the sound level at the observers ears should be higher with the horn than without the horn.

What if their claim that using the horn causes a perceived 4x increase in loudness is true?  (Loudness is a perceptual quantity, where sound level - either sound pressure level or sound intensity level - is a measured quantity.)    Then, the only mistake that they made is equating a 4x increase in loudness with a 60 dB gain in sound level.  Here's a graph from a lab we do in my "Sound and Acoustics" class:

In this lab students hear a broadband tone which they assign an arbitrary loudness level rating. In this class, we all agreed to call the reference tone (relative sound level = 0 dB) a loudness level of 100.  Note, there are no units, since it's an arbitrary scale we made up for the lab. Then they hear several other tones where the level has been increased or decreased randomly and they are asked to rate the loudness of the tone with respect to the loudness of the reference tone.  

What I've plotted above is the class average of loudness level vs the actual relative sound level (in dB) for all trials.  Each sample was presented twice (not in sequential order) so the scatter is a sort of approximation to the uncertainty in the measurement.  The solid line represents a model that is what we would expect to see for a larger sample of the population.  For such a small class, the trend is pretty close to the "expected" behavior.

Note that a 4x increase in loudness, from either 25 to 100 or 100 to 400, corresponds to a relative gain in sound level of 20 dB, not 60 dB.

Under ideal testing circumstances, I could believe that a passive amplifier like the horn amp would give a 20 dB gain right in front of the horn.  But someone should have caught the 4x = 60 dB nonsense.

What does $200 get you these days?

This May our department is offering two sections of the "Sound, Music, and Hearing" class, which fill a general education requirement for Physical Science Labs for non-science majors.  It's a fun class to teach because we get to play with a lot of fun toys and do a lot of neat experiments that we don't often have time to cover in the general physics labs.

The professor teaching the other section and I decided that we wanted some new resonance tubes with the water reservoir attached to a stand for looking at standing waves in a closed-open tube.  The CENCO (or is it Sargent-Welch?) catalog had the best deals, but they also had the largest variety of resonance tube experiments to order.  Our budget is only a few thousand dollars, and as much as we'd like to have 4 resonance tubes for the class, we decided to order one of the low cost models (the Student Resonance Apparatus) and one of the mid-range models (the CENCO Resonance Apparatus).  I placed the order a week ago and recently some boxes appeared in the main office.

I opened the box and removed all the packing material.  The kit was nicely packaged.  All the clamps and the reservoir and rubber tube was all in a ziplock bag. The aluminum rod was taped to the cardboard tube which contained the acrylic tube. I pulled the instructions out of the bag and worked on assembling the apparatus.

Assembly was straightforward. The rod screws into the base, then the clamps are attached and the tube is slid into place. My only complaints were that the rod was not perpendicular to the base (it must have been tapped a little crookedly) and that the instructions kept referring to the "tripod".  I don't know about you, but when I see the word "tripod," I instinctively think of something with three legs and not a flat base.



Here's a photo of the assembled resonance apparatus. The tube is quite long, meaning we should be able to get lots of standing waves in the tube for a large variety of tuning forks. I cheated a little bit with the photo by choosing an angle that does not draw attention to the lean of the rod.  One of the features that was kind of nice about this apparatus is that the bottom of the tube has a peg which fits into a small hole in the base to keep the tube well positioned. Also, this apparatus includes a clamp for holding a tuning fork above the resonance tube. The clamp is just a right angle clamp, which was a little disappointing that it wasn't anything more specialized, but it will be interesting to see if the  clamp works well to hold the tuning fork while the fork is vibrating.


After setting up the mid-range model, I unpacked the economy model.  The contents of the shipping box are shown in the following photo.

It may be hard to tell from the photo, but there was an excessive amount of packaging for this kit. All of the pictured components were in a single box stuffed with packing paper. The base and the tube/rod came in separate boxes.  And the bag with all of the clamps and reservoir were in a plastic bag, which was so tightly taped shut that I had to destroy the bag just to free its contents. (On Earth Day, of all days...)


After I made it through all of the layers of packaging, assembly of the economy model was as easy as the mid-range model. The tube is held to the rod by a test tube clamp and there is no clamp for the tuning fork.

The economy model uses what is essentially a large plastic cup (complete with the SOLO logo on the bottom) for the water reservoir. One wonders how much abuse the reservoir will be able to stand. I suppose that if it is damaged, replacement would not be too difficult or costly.

The economy model does not have a peg on the bottom to help keep the tube in place on the base. like the mid-range model does.

Also, the economy model is significantly (~50%) shorter.

Here is a photo of the two models side-by-side for comparison:


You can easily see the difference in the height of the two.  Also, the lean of the longer tube is more apparent when comparing the two.

The real question is how do the two compare in terms of using them to do experiments.  I haven't had a chance to try them out yet, but I have made some observations from putting them together.  The real question is: What do you get by spending the extra $200 to go from the economy model to the mid-range model?

From what I have seen you get the following benefits:

• Longer tube, meaning a wider range of frequencies to work with.
• Sturdier water reservoir.
• Peg in the base to better hold the tube in the apparatus
• Clamp to hold the tuning fork on the rod
• The machining of the hose connections is clearly of a higher quality. (Need closeup photo to show.)

There are some advantages to the economy model, for instance:

• Shorter tube means experiments could potentially be done on the lab table, instead of on floor.
• Less expensive components means lower costs for maintenance.
• The smaller size may be easier to store.

I'm going to have some fun playing around with both models in the next few days as we continue to get ready for May Term.