Tag: frequency

Posted in Science & Nature

Belling The Cat

Posted on by Jinavie

There once lived a community of mice in the attic of a house. The mice would sneak into kitchens, gnaw holes in the walls and run about freely. The owners were so fed up that they brought in a cat, causing the mice to all hide in fear. The terrified mice eventually held a meeting to discuss how they would sneak around the house without getting caught by the cat. One mouse suggested: “What if we put a bell around the neck of the cat? Then we can hear it coming and run away.”. The mice unanimously agreed that it was a brilliant idea. However, when they came to decide who would bell the cat, no mouse was brave enough to step forward and the plan was never carried out.

What would actually happen if a cat was belled? Without a doubt, the cat would take it as a cruel, cruel punishment. Not because it cannot catch mice, but because the sound of the bell ringing every time it moves will be extremely loud for the cat. A cat’s hearing is six times better than a human’s. With this excellent hearing, the constant sound of bells attacking its eardrums would be physical torture for the cat.

Furthermore, a cat can hear frequencies as high as 40,000Hz. A person can only hear up to 20,000Hz, meaning a cat hears over twice the range of sounds we can. This combined with the boosted volume results in the cat living in a very noisy world. Ergo, putting a bell around a cat’s neck is an extremely atrocious thing to do.

Posted in Science & Nature

Cryptography: Frequency Analysis

Posted on by Jinavie

A cipher is a message that has been encoded using a certain key. The most common and basic type of ciphers are encrypted using letter substitution, where each letter represents a different, respective letter. For example, the message may be encoded in a way so that each letter represents a letter three values before it on the alphabet (e.g. if a=0, b=1… “a” becomes “d”, “b” becomes “e” etc.). This creates a jumble of letters that appears to be indecipherable.

However, the characteristics of substitution ciphers make them the most decipherable type of encryptions. As each letter can only represent one other letter, as long as the key is cracked (i.e. what letter is what), the message and any future messages can be cracked. The most important tool in decrypting substitution ciphers is pattern recognition and frequency analysis.

Frequency analysis relies on the fact that every language has certain letters that are more used than others. In the English language, the letters that are most used, in order, are: E, T, A, O, I, N, S, H, R, D, L, U (realistically, only E, T, A, O are significant and the rest are neither reliable nor useful in frequency analysis).

For example, if Eve intercepted a long, encrypted message that she suspects to be a simple substitution cipher, she will first analyse the text for the most common letter, bigram (two letter sequence) and trigram. If she found that I is the most common single letter, XL the most common bigram and XLI the most common trigram, she can ascertain with considerable accuracy that I=e, X=t and L=h (“th” and “the” are the most common bigram and trigram respectively). Once she substitutes these letters into the cipher, she will soon discover that certain patterns arise. Eve may notice words such as “thCt” and deduce that C=a, or find familiar words and fill in the blanks in the key. The discovery of each letter leads to more patterns and the vicious cycle easily breaks the code.

Frequency analysis is extremely useful as it can be used to attack any simple substitution ciphers, even if they do not use letters. For example, in Sir Arthur Conan Doyle’s Sherlock Holmes tale The Adventure of the Dancing Men, Sherlock Holmes uses frequency analysis to interpret a cryptogram showing a string of hieroglyphs depicting dancing men.

To reinforce this weakness in substitution ciphers, many cryptographers have devised better encryption methods such as polyalphabetic substitution, where several alphabets are used (e.g. a grid of two alphabets – also called a tabula recta).

Posted in Science & Nature

Resonance

Posted on by Jinavie

The power of vibration is incredible. Vibration allows a microwave to heat food and causes cities to be destroyed by earthquakes. The most interesting feature of vibrations is resonance, where a vibration of certain frequency greatly amplifies the vibration of another object. Every object has a natural oscillating frequency and when another wave of the same frequency hits the object, the oscillation suddenly amplifies and resonance occurs.

The best example for resonance is a swing. If you push a person on a swing at the same frequency as the swing’s natural frequency, you can achieve a much greater height than from pushing at any other frequency. Resonance can also be used to shatter a glass with only sound, by singing a sustained note at the same frequency as the glass’ natural frequency.

Resonance is how two things combine to create an even greater force.

1 + 1 = 3

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Posted in Science & Nature

Cricket

Posted on by Jinavie

The sound of crickets in the autumn night is quite inspiring. Only male crickets can make this clear and beautiful sound, by rubbing their serrated wings against each other.

There are four kinds of cricket chirps: an attracting song (for females), a courting song (when a female is near), an aggressive song (when a male is near) and a copulatory song (after a successful mating). Each song is played at a different volume and pitch.

As all insects are cold-blooded, they are heavily affected by temperature. In the case of crickets, this is reflected in the frequency of chirps, which increases proportionately to the temperature. Using this, one can calculate the air temperature from the number of chirps a Snowy Tree cricket makes (count the number of chirps in 14 seconds plus 40 to get the temperature in Fahrenheit).

Finally, cricket chirps cannot be heard via cellphones. This is because a cricket chirp is usually around 6500Hz frequency, while most cellphones operate at a maximum of 3300Hz.