# how is a tuning fork used to calibrate a radar gun?

On past occasions I have seen reference to the use of a tuning fork for calibrating the radar guns used by police to measure vehicle speeds.

How does that work?

Tons of legit info out there.

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When the fork is tapped, the ends vibrate at a specific frequency. The radar beam bounces off of the metal, and is doppler-shifted by the movement. This shift gives a ± velocity reading, just like a moving vehicle would.
Presumably, the radar gun ignores negative velocities.

The procedure? Or the physics?

Prior to patrol, the officer takes out a couple certified and calibrated tuning forks; each preset to a specific frequency. He strikes the fork and holds it in front of the radar gun to verify that the gun is reading the correct speed for that fork. He does this with 2-3 forks, verifying the speed of each. This certifies that the gun was still in proper calibration prior to its use. He/she isn’t actually calibrating the gun, just verifying the calibration. That way, the defense attorney can’t try to argue that the gun might have been malfunctioning.

As for the physics: The fork is actually vibrating at a specific speed because of it’s size and density. If it is vibrating at 45 mph (whatever hz that happens to be), the gun should read that 45 mph when that fork is placed in front of the gun.

The physics is what I’m curious about.

This is wrong. The fork will vibrate at a predetermined frequency because of its material and geometry. But the instantaneous speed is constantly varying, and the peak speed will vary with the amplitude of the vibrations: a large amplitude (which manifests as louder sound) means a higher peak velocity.

Sorry, I meant to include a caveat on the physics part. I am familiar with the procedure but only have a layman’s understanding of the physics which is why I asked which you were interested in. I tried to give my best understanding of that part. I had practical experience with the former during my academy and internship days. You’re obviously asking a more advanced question about the complexity of the physics and someone knowledgeable should be in here shortly to clarify that part for both of us. So, your’re asking how it works to calibrate a speed, since the speed actually varies while it vibrates?

When you say, “material” and “geometry”, that basically density and shape, right? Isn’t it the density of the material that matters? And shape matters, but not size? I thought smaller ones (all else being equal) were higher frequencies. Now you have me curious.

Pretty much, yup. That’s a bit of a puzzle to me.

This seems to answer one of my great questions of life, if one can design a car that vibrates at a certain frequency, would that make it basically immune to radar tickets? It would seem yes, such as have that vibration at 350 mph, so if going a reasonable 100 mph, it, after reading such vibration of lets say 350 mph, read a unreasonable speed from 250 to 450 mph, depending on direction and cosine, according to the posts so far.

This is going to be a bit technical, so let me know if you need something explained further.

Modern radar guns basically use what is called a heterodyne receiver. This type of receiver “beats” the received frequency against the transmitted frequency, with the result being kind of a “difference” signal called the Intermediate Frequency (IF).

The radar gun then executes what is called a Fast Fourier Transform (FFT) on the IF, which ends up with a bunch of little “data buckets” corresponding to different frequencies.

This is a bit math-heavy for a typical wikipedia page, but it explains what a FFT is in more detail:

Radar guns operate at about 10 to 30 GHz or so. There are different specific frequencies that they use within this range. The speeding object shifts this frequency (google Doppler shift). So, let’s say 55 mph works out to a frequency shift of 5000 Hz (that’s not the real frequency, but I don’t feel like calculating out the actual number). If you want to fake out the radar gun, you use a tuning fork that is also tuned to 5000 Hz. Then, when the radar gun executes its FFT, it ends up with a strong signal in the 5000 Hz bit bucket. So it thinks that it received a signal return from an object going 55 mph.

The tuning fork is not intended to provide a Doppler shift (which would be meaningless - as the fork vibrates its speed varies as a sine function, thus varying from positive to negative velocities and crossing through zero - and the angle of incidence would be critical as well.)

Speed radars do look for the Doppler shift, but the trick is to understand how they detect it. A fixed frequency is transmitted, and a reflected signal received. If you mix the two signals together you will get a hetrodyned set of frequencies out of the mixer. Sum and difference of the inputs. If you low pass filter the mixer output you will get a signal which has a frequency that is the amount of the Doppler shift. For something as slow as a moving vehicle this is not a large shift. Microwaves in the GHz, times vehicle-speed/c = something in the few kiloHertz.

Now point our radar gun a vibrating tuning fork. You will get a reflected signal, but you will get a signal that has been modulated in intensity by the frequency of the fork vibrations. This isn’t a Doppler shift, but it will end up popping out of the radar gun’s internal mixer in just the same way as the Doppler shifted signal will. What you are doing is ensuring that the frequency to speed conversion done on the detected signal is correct. Back in days of yore that conversion was done with analog circuitry, and could drift. Nowadays you would do the whole LF end in software, and there would be no calibration needed.

Bah! Ninja’d.

Specifying “material” locks down both the density and the elasticity of the material, both of which are important for vibratory behavior. For example, aluminum has lower density than steel, so you’d expect an aluminum tuning fork to vibrate faster than a steel one. But aluminum also has a lower modulus of elasticity (i.e. it flexes more under a given load), which tends to offset the effect of that lower density, at least in regards to determining vibration frequencies.

Specifying “geometry” locks down both the shape and the size, which together determine both the mass and stiffness of the oscillating parts.

Nope, got it, thanks. Did a nauseating amount of work with FFTs in grad school.

The key thing I think I was missing is that the tuning fork is “spoofing” the radar gun; that clears things up nicely.