Wave Interference and Beats - Sound Waves and Electromagnetic Waves


(Note: Please refer to this page for light interference and the Young experiment as well as for mechanical wave interference. You may find interesting this page on "the ear as a frequency analyzer".)


Part Ia : Sound Waves – Human hearing range and musical tones


Humans hear sounds from 20Hz to 20000Hz


Test your lower and upper limit with this video:



Pure tone and Musical tone

A pure tone is a tone with a sinusoidal waveform, e.g. a sine or cosine wave.


Traditionally in Western music, a musical tone is a steady periodic sound.


A simple tone, or pure tone, has a sinusoidal waveform. A complex tone is any musical tone that is not sinusoidal, but is periodic, such that it can be described as a sum of simple tones with harmonically related frequencies.[2]


A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre(or quality).[1] The notes used in music can be more complex than musical tones, as they may include aperiodic aspects, such as attack transients, vibrato, andenvelope modulation.




Musical notes

Do, Re, Mi, Fa, Sol, La, Si

C, D, E, F, G, A, B



Piano Key Frequencies


The first Do or C of a piano has a frequency of 65,41 Hz. You can find the frequencies of all the piano keys at this wikipedia link (there is also an image that can be downloaded. Here is an interactive piano and the associated frequencies (adjust the knobs to another position than the default e.g. as shown in the image below).

At the picture of the piano further down we start with the C2, and we also have C3, C4 and C5. Note that the A4 or A440 is termed "pitch standard" and serves as a general tuning standard for musical pitch. This is also the default for the tone generator online tool that will be mentioned further down.



Oscilloscope - Piano




Note the sine wave with a frequency of 65.41Hz corresponding to the marked key (Dp or C).


Part Ib: Beats and Sound Waves


Someone says 'this music has a fast beat" meaning that one beat follows quickly after another. We refer to "beat" as the action of beating for instance a drum in a repetitive way. It is actually an alternation of loud and soft.


Also, in some cases a police car siren does not make a continuous sound, it makes a beat, a sound that goes from loud to less loud.


The definition of a beat is :"a rhythmic interference of close frequencies". We basically sum up the two waveforms and this results in parts where they reinforce each other so that we hear a loud sound and parts where they cancel each other out and we hear a weak sound. The alternation of loud and weak (or sound and no sound) gives us the impression of "beat".


Generate a beat from two tones using the http://onlinetonegenerator.com/ as mentioned in the following video https://youtu.be/i886Lbjbl9k (duration: 2min12s). Generate a tone of 440Hz (pitch standard for musical instruments) and at another browser window a tone of 441Hz. You will hear the beat and you can explore this further with the video mentioned further down.




Part Ic: Finding the Beat Frequency for Sound Waves

The four screenshots of the figure are copied from this video.
1. Using the intenet page http://onlinetonegenerator.com generate a 440Hz tone and a 441Hz tone (as mentioned in the video above.)
2. Let us assume that they are represented by the blue and the pink wave (e.g. top left). Can you confirm that their frequency is slightly different ?
3. Create an overlap which just means place the two beginnings together. You will get the figure on the bottom left.
4. Add them algebraically. You will have the yellow dotted line.
5. Let's describe their overlap, their interference: they start by constructive interference, which means « loud », they proceed with destructive interference (« soft ») and they end with constructive interference again (« loud »). This is one full « wobble » circle - let us refer to a « wobble » of a siren for instance -- and represents one beat.
6. What is the beat frequency? You can find it by taking the difference of the two frequencies of the overlapping waves. If we have a 440Hz tone and a 441Hz tone, what will be the beat frequency? How many « wobbles » will we hear per second? You can confirm your answer with the above facebook post.
7. Please note the complex waveform pattern generated from the two initial waves.



@infobook tweet

Wave Interference & Beats: Generate a 440Hz & a 441Hz tone and listen to their beat that repeats itself every 1sec http://goo.gl/aA1MvO 


@infobook tweet

Humans hear from 20Hz to 20000Hz.Test limits w/ this video https://youtu.be/qNf9nzvnd1k  #Infrasound #Ultrasound Pitch standard (tune)=440Hz A440


@infobook tweet

The first key of the piano, a C or Do represents a frequency of 65.41Hz.Try this piano https://goo.gl/0rKbxd  cited:http://goo.gl/aA1MvO 




Part II: Beats and Electromagnetic Waves


Consider an electromagnetic wave of a frequency of 10533 MHz and another with a frequency of 10532 MHz. What will be the result of the interference of these? A wave with a frequency of 1MHz.


The two waves will beat against each other and they will produce a beat of 1MHz.

Watch the measurements at this 1:50min video https://www.youtube.com/watch?v=u_nmvA5KOkQ




Figure: One horn produces 10533 MHz waves and the other produces 10532 MHz waves. The researcher covers each of the two with his hand and verifies their emission using instrumentation.




Figure: The oscilloscope demonstrates the detected waveform. Upon interference (beats) a wave of 1096 Hz (1MHz) is measured.



The same phenomenon can be observed at this MIT video:




@infobook tweet