Eng: High and low frequency sound

The 'cat piano' never happened. The idea was that each key dropped a hammer on the tail on the tail of a carefully-tuned cat, generating a high note. If you try this gadget, you are likely to end up in court. Don't do it!

Good hearing

Humans can hear sounds as low as about 15 vibrations per second, a tone we call 15 hertz or 15 Hz. Teenagers can hear tones as high as 20 kHz, 20 kilohertz, or 20,000 hertz, but after your teens, your hearing slowly gets worse, as you stop hearing the highest tones.

By the time you are thirty, you will only be able to hear 15 kHz, or even less, if you have been exposed to a lot of very loud music. By the time you are sixty, you will hear little above 10 kHz, and by the age of seventy, your upper limit will be about 6 kHz, not much more than the highest note on a piano. Bats and porpoises can make noises as high as 120 kHz, and they can hear 150 kHz. Dogs can hear tones as high as 50 kHz.

Ultrasonic sound

Ultrasound is any sound with a frequency greater than 20 kHz. Depending on the frequency, some animals can hear some ultrasonic tones, and we use ultrasound in medicine because some very high frequency sounds are reflected back to different extents by different materials, such as some of the tissues in the human body. Medical ultrasound is usually in the range 3 to 10 megahertz.

This provides a way of getting safe and undamaging images of internal structures, which can deliver clear views of foetuses, but ultrasound is also used in engineering for things like detecting cracks in railway lines. The ultrasound pulses are produced by high-frequency transducers using the piezoelectric effect. (Now you have the technical words, you can look them up.)

To make ultrasound at home, get some lengths of 2 cm steel rod, ranging from 30 cm down to about 5 cm, and the loan of a cathode ray oscilloscope (or CRO), a microphone, an amplifier, and some string. (Why do I think you might have some trouble doing this one at home? No matter—push somebody hard enough, and you may be able to borrow the gear.)

The longest bar will ring at an audible frequency when struck, but the shortest piece will vibrate at about 30 kHz. This ringing will be inaudible, but the microphone and CRO will reveal that the ringing is still there, even though we cannot hear it.

(If you want a cathode ray oscilloscope on your smart phone, try searching the web with this string: <cathode ray oscilloscope apps audio>.)

Shorter objects vibrate at a higher frequency. The effect will depend on the steel selected, so do some experimenting before you try this. It will help if you strike each piece of steel in its centre with a small rubber or wooden mallet.

Low frequency sound

A French scientist, Marin Mersenne, was interested in sound frequencies. If you pluck a stretched string and watch it, all you will see is a blur, how could you possibly count the vibrations? The answer is simple if you know that longer plucked strings give lower frequencies. Double the length of any string and you halve the frequency.

Big may not always be beautiful, but it is often attention-getting. Mersenne’s ‘plucked strings’ were a hemp rope more than 30 metres long, and a brass wire 43 metres long. With that sort of length, the vibrations were slow enough that he could see each individual wave.

By varying the length and the tension on these giant strings, Mersenne was able to find a formula that tied the frequency of a string to the length, the tension, and the mass of one metre of any wire or string.

He could now predict what the frequency of a stretched wire would be, even if the frequency happened to be too high to count. In this way, Mersenne found that the frequency of an organ pipe was 150 Hz, by tuning a wire to match the pipe, and then calculating the frequency of the wire.

Mersenne wrote up his work with this dramatic introduction: “A deaf man may tune a lute, a viol or a spinet and other stringed instruments… if he knows the length and the mass of the strings.”

Note:

The frequency n of a stretched string is inversely proportional to the length, and it is directly proportional to the square root of (the tension divided by the (mass per unit length)).

So you can halve the frequency if you do any one of:

* double the length;

* reduce the tension by 75%; or

* quadruple the mass per unit length (meaning double the diameter).

That’s all you get on this one. Why should I do all the work? Play with it!

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