Musical thirds in heater hose

The heater hose has a resonant frequency based on its length. This is the same principle used by trumpets and trombones - the player gets higher notes by simply blowing harder, and the tube provides the miusical overtone series. The overtone series is octave, fifth, major third, minor third, slightly less than minor third.

The broken heater hose should be able to produce most bugle tunes like taps, reveille, if only the car is driven in an appropriate manner!

The heater hose explanation does not explain specifically why the tones would be heard at 2000, 2500, and 3000 rpm, as the caller claimed. However, if there is some mechanism that has a frequency of vibration that is either the same as the motor’s rpm’s or at least correlated with it, then here is what could happen.

A vibration of 500 cycles per second would produce some tone (it’s sound would be a little higher pitch than the musical A 440). Increasing the rate of vibration in integer multiples is what produces the harmonic series.

In that series, if you start from a base tone of 500 cps, then 1000, cps would be exactly an octave higher, 1500 an octave plus a fifth, 2000 exactly two octaves, 2500 would be two octaves plus a major third, and 3000 would be two octaves plus a fifth.

In other words, the sequence of notes that would be produced at 2000, 2500, and 3000 rpm would be exactly a major triad chord, which ascends from its root tone up a major third and then another minor third (do, mi, so), just as the call said (she said the first jump was a minor third, but she didn’t sound too sure of that).

How you would get vibrations coming from the heater to be correlated with the rpm’s is something for the boys to explain.

If you doubt my credentials to give such an explanation, I have a bachelor’s degree in music education, although now I am an academic psychologist (a researcher, not a shrink), and in between I was a chef. So I am either a renaissance man who should know everything, or a pathetic schlubb who can’t hold a job. Take your pick.


— Cogprofessor

I had a similar experience while adjusting the drive motors on a telescope. Telescopes use very precise motors to move the telescope slowly to track the sky as it rotates. Years ago the boys used to ask for puzzler answers to be written on a Meade LX200 telescope, which is one of the nicer modern amateur telescopes with computerized drives. This was an older Meade LX10 with simple dc motors, regulated by a voltage regulating circuit, with some speed adjustment by a variable resistor (“trim pot”). As I tweaked the speed, I found that the pitch (indicating drive speed) seemed to want to shift from one speed to another distinctly higher rather than varying smoothly as I adjusted the trim pot.

My best guess is similar to the previous comments: the drive runs more efficiently at certain resonant frequencies. At “dissonant” frequencies in between, it wouldn’t run very efficiently, so it would take a lot more power. So if I increased the trim pot only slightly, that wouldn’t be enough additional power to run at a dissonant frequency, so the drive would stay near its original speed, or just a hair faster, until I increased the trim pot enough to run at the dissonant frequency, but that may be even more than needed for the next efficient resonant speed (even if that’s faster than the dissonant speed in between), so it jumps to that next efficient harmonic instead.

I also had the same inspiration one of the boys had when he used the term “quantum leaps” to describe this. I suspect in the future when we really understand quantum physics (as opposed to being the hodgepodge of inspired guesses it currently seems to be), we will find that this is why the universe, on a tiny scale, seems to work in discrete jumps rather than being continuously variable.

I used to go to elementary music classes to demonstrate the French horn. One thing I did was that I had an old section of garden hose that I cut to the length of the horn. I would play a passage from a Mozart concerto on the garden hose, then on a valveless horn and finally on a modern horn. This would fascinate the kids.
Thee is a recording that I have of the late Dennis Brain (1921-1957) playing movement of a Leopold Mozart concerto on a garden hose.

Was that a linear or logarithmic potentiometer?

Hoping it is related, I am not a musician but have played with various musical instruments. I have noticed you can get 2 different pitches on clarinet and flute depending on how hard you bl ow. It is a or b, not a progression. Is this a possible explanation?

I am a professional physicist and an amateur singer. The frequency ratios are exactly as cogprofessor said.

The reason the hose oscillated at these frequencies is happy accident. Imagine a micro-crack at some point in the hose. As the car vibrates slightly (at its rpms) that oscillation causes the microcrack to subtly change shape allowing air in at a paricular frequency.

Based on geometry of the vacuum hose only certain frequencies will oscillate resonantly. The frequency that will take most of the energy is the resonant frequency closest to the forcing frequency.

So cogprofessor + barky dog + all the other comments here together make the complete answer. If you knew the location of the leak, the geometry of the hose, and what the hose is connected to you might be able to work out what the frequencies are.

I think some of the listeners commented on the geometric progression. If you ever played a trombone or bugle this is easy to demonstrate. On a Bugle you have no valves, just a conical tube and a mouthpiece. The mouthpiece makes a vibration and how hard you blow or pinch the embouchure determines the vibration. Everything in the world has this overtone scale. Which usually starts with an octave then fifth, 4th maybe, a bunch of thirds and then the intervals get smaller as the frequency gets higher. This is what is happening in the hose which is just an accident of pressure and vibration in this case but is a natural phenomenon.

The typical vacuum system on a car with a leak is (I believe) open at both ends (the venturi & the leak). The flute is also open at both ends with the lowest note (fundamental) at twice the length divided by the speed of sound (2L/v = 25.6" at Middle C). (The Saxophone, which is closed-at-one-end-conical has the same harmonic series). The pitch at 500 would be a slightly flat “c” (middle of treble clef=C5=523.25 Hz). At 500 Hz at the 3th Overtone (4th Harmonic) would give a fundamental length of about 51.5 inches. The harmonic series up that high (the 3rd, 4th & 5th overtone) would produce the tonic, third & fifth that you would hear. Any lower than that, probably wouldn’t be loud enough (insert alto or bass flute sound here…), and any higher than that would be a flattened minor 7th–the energy required to get that high would be almost twice it would be to get to the 5th, and so the engine & road-noise would be so loud that you wouldn’t hear, either.

With a closed-at-one-end-cylinder, similar to a clarinet, the frequency would be measured at the speed of sound divided by 4 times the length (4L/v). This would produce a series that would skip every other partial. (ie: Fundamental, octave+5th, 2octave+3rd, 2octave+(flat)7th, etc.) At approximately 500 Hz, with a purely cylindrical tube, playing the 7th, 9th, & 11th overtones, would give a (fundamental) length of around 45.3 inches. And the Overtones would sound very out of tune… (Flat minor 7th, Major 2nd, and Sharp Augmented 4th)

It could also be a chamber of some sort (with a linear length around 50") where the wind is brushing past the opening (Could be anything/anywhere–the ear cochlea is a spiral to take up the least amount of volume). Could be a hollow bumper, closed-off wheel well, hole in the trunk, etc. All it would take would be the wind rushing over the hole at a certain angle (like blowing a bottle) to produce it.

The Formant is one of the frequencies a system amplifies naturally–such as motor noise, piece of wood, bathroom/stairwell singing, etc. It could also be a loose piece that vibrates at those frequencies, although the harmonic series is much different (similar to chimes): octave= 1.414 times the length (root of 2 - not 2 times the length, as with strings and air).

Since the speed of sound is constant (0 to 10000 ft = change around 3.55%; humidity = change 0.1%-0.6%, etc ), if you could determine the pitch, you could probably find the source.

Love the Puzzlers!!!

Paula’s Bronco with the perfect pitch. I’m doubting the vacuum hose or heater hose explanation. It could be the fuel pump like Tom and Ray said, but I think it is noisy fuel injectors. Here’s my case:

Injectors do make a noise. A loud noise. But when they are fully seated the noise stays mostly in the intake manifold. Anybody who’s ever pulled them out of the intake manifold to test them, you know they are really quite loud in operation. And they make a musical-like sound, with a clearly indentifiable pitch. I’m not sure of the orientation of the engine in Paula’s Bronco, but on transverse mounts, the fuel injectors usually face back toward the passenger compartment, and the noise is heard more easily inside the car with the windows up (so it’s quiet) than from standing in front of the car with the hood up, where the rest of the engine noise masks the fuel injector noise.

If you have a transverse fuel-injected engine car, I’ll bet you can hear your own fuel injectors if you listen carefully. Even if you’ve never heard them until now. Try it. With the windows rolled up, the radio and fans off–try to make the inside of the car as quiet as possible – now listen carefully as you accelerate, like when you enter a freeway on ramp. You’ll hear exactly what Paula is describing. High pitched musical tones coming from what appears to be under the dashboard. That’s the fuel injectors singing their siren-like tune. Good for them, as it means they’re working.

There’s a few things I don’t understand however:

I don’t have an explanation for the tones increasing by musical thirds. On cars I’ve heard this sound, the pitch seems to go up directly with rpm, and gets louder the higher the pitch becomes. But it may be that the Ford electronic Fuel Injection scheme’s timing of injector release results in musical thirds. Who knows?

And I don’t have an explanation for why Paula is only now hearing this. Possibly it could be that the noise has been there all along, but she heard it distictclyu for some reason or another, and is now tuned-in on it. This happened to me. I never noticed the sound of the injectors until one time I had to pull them out and test them. After that, and forever after, I notice them singing, especially on acceleration. It could be that one or more of the injectors has become loose. Or it could be that one or more of Paula’s injectors has clogged up a bit, which could increase the noise level. & Anything affecting the fuel pressure at the injector rail would affect the noise level, like a fuel pump problem, a fuel pressure regulator problem, or signals that modulate the fuel pressure, like Ray mentioned, engine vacuuum.

I admit it’s a wild guess. But what do you think? Could it be the Bronco’s fuel injectors that Paula is hearing?