Demonstration Of Beat Frequency Engineering Essay

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Beat is an interference between two sounds of slightly different frequencies, supposed as periodic variations in volume whose rate is the difference between the two frequencies.

Beats produced by tuning instruments that can produce sustained tones can easily be recognized. Tuning two tones to a unity will present an irregular effect: when the two tones are close in field but not yet matching, the difference in frequency creates the beating. The volume varies as the sounds alternately interfere constructively and destructively. When the two tones gradually approach harmony, the beating slows down and disappears, giving way to full-bodied harmony resonance.

Mathematics and physics of beat tones:-This concept exhibits acoustically. If a graph is drawn to show the function corresponding to the total sound of two strings, maxima and minima are no longer constant as when a pure note is played, but change over time: when the two waves are nearly 180 degrees out of phase the maxima of each cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the superficial volume.

the successive values of maxima and minima form a wave whose frequency equals the difference between the two starting waves. Let's see simplest case, between two sine waves of unit amplitude:

If two starting frequencies are quite close the frequency of the cosine of the right side of the expression above, that is [(f1−f2)/2], is often too slow to be supposed as a pitch. Instead, it is supposed as an episodic variation of the sine in the expression above whose frequency is (f1 + f2)/2, that is, the average of the two frequencies. the sine part of the right side function interchanges between negative and positive values many times during one period of the cosine part, only the absolute value of the envelope is applicable. Therefore the frequency of the envelope is twice the frequency of the cosine,so the beat frequency is:

fbeat = f1 − f2

This can be seen on the diagram on the right.

A physical explanation is that when equals one, the two waves are in phase and they interfere constructively. When it is zero, they are out of phase and interfere destructively. Beats occur also in more complex sounds, but calculating them mathematically is difficult

Difference tones

If there are two waves first in harmony, f1 − f2 = 0. As the difference between f1 and f2 increases, the speed increases. Beyond a certain proximity (usu. about 15 Hz), beating becomes unnoticeable and a unevenness is heard in its place, after which the two pitches are supposed as separate. If the beating frequency rises to the point that the envelope becomes audible (usually, much more than 20 Hz), it is called a difference tone

Binaural beats

Binaural beats are heard when the right ear listens to a slightly different tone than the left ear. Here, the tones do not interfere physically, but are summed by the brain .This effect is related to the brain's ability to locate sounds in three dimensions. binaural beats can have a psychological effect upon the listener.

Binaural beats

Acoustical background

Interaural time differences (ITD) of binaural beats

While at time of localizing 2nd wave the human hearing arrangement analyses interaural time differences between both ears inside small frequency ranges, called critical bands. For frequencies below 1000 to 1500 Hz interaural time differences are evaluated from interaural phase differences between both ear signals. The perceived sound is also evaluated from the analysis of both ear signals.

Exposure to binaural beats in an environment of restricted stimulation coupled with a guidance process can safely provide access to and experiences in many propitious states of consciousness. This method requires a unique combination of well-understood psycho-physiological inductive

techniques with the addition of a refined binaural-beat technology. Binaural beats provide potential consciousness-altering information to the brain's reticular activating system. The reticular activating system in turn interprets and reacts to this information by stimulating the thalamus and cortex -thereby altering arousal states, attentional focus, and the level of awareness,

i.e., the elements of consciousness itself. This effective binaural-beat process offers a wide variety of beneficial applications and vehicle for the explorationof expanded states of consciousness

Beat in music:-beat is elementary time unit of music,  the pulse of the mensural level, also known as the beat level,but as beat is related with rythems ,this term describes order of individual beats


Subjective Tones

When two single-frequency tones are present in the air at the same time, they will interfere with each other and produce a beat frequency. The beat frequency is equal to the difference between the frequencies of the two tones and if it is in the mid-frequency region, the human ear will perceive it as a third tone, called a "subjective tone" or "difference tone". The difference tones are always present, but they can be made prominent by using two high, clear tones like the notes of a flute. With two flutes you can produce a "trio for two flutes". This phenomenon can also be produced with one brass instrument (multiphonics). If a French horn player plays one note and hums another, then the subjective tone which is the difference between them can sometimes be heard clearly.

One important role of subjective tones is the missing fundamental effect whereby a correct sense of pitch for a musical sound may be maintained even if the poor fidelity of the sound reproduction has filtered out some of its lower harmonics.

Missing Fundamental Effect

The subjective tones which are produced by the beating of the various harmonics of the sound of a musical instrument help to reinforce the pitch of the fundamental frequency. Most musical instruments produce a fundamental frequency plus several higher tones which are whole-number multiples of the fundamental. The beat frequencies between the successive harmonics constitute subjective tones which are at the same frequency as the fundamental and therefore reinforce the sense of pitch of the fundamental note being played. If the lower harmonics are not produced because of the poor fidelity or filtering of the sound reproduction equipment, you still hear the tone as having the pitch of the non-existant fundamental because of the presence of these beat frequencies. This is called the missing fundamental effect. It plays an important role in sound reproduction by preserving the sense of pitch (including the perception of melody) when reproduced sound loses some of its lower frequencies.

The presence of the beat frequencies between the harmonics gives a strong sense of pitch for instruments such as the brass and woodwind instruments. For percussion instruments such as the cymbal, the sense of pitch is less definite because there are non-harmonic overtones present in the sound.


One of the applications of subjective tones is the production of three tones by a single brass player. The player plays a note in the usual way but in addition hums a second note into the mouthpiece. The beat frequency between these two notes produces a third tone. Such tones are sometimes called multiphonics.

Police RADAR

RADAR speed detectors bounce microwave radiation off of moving vehicles and detect the reflected waves. These waves are shifted in frequency by the Doppler effect, and the beat frequency between the directed and reflected waves provides a measure of the vehicle speed.

Doppler Shift, Moving Target

The Doppler shift for relatively low velocity sources such as those encountered by police RADAR is given by

but in this case there are two shifts: one because the wave incident on the moving car is Doppler shifted and an additional shift because the reflection is from a moving object. The frequency shift of the reflected wave received at the source of the wave is

This shift is detected by measuring the beat frequency with the transmitted wave.

Beat Frequency and Speed

The beat frequency between a microwave transmitted signal and a reflected signal off a moving object is

where the target velocity is taken as positive if the target if approaching the transmitter. Police RADAR uses this method for measurement of auto speed.

Calculation of speed

Doppler Pulse Detection

The Doppler effect in an ultrasonic pulse probe detects the reflected sound from moving blood. The frequency of the reflected sound is different, and the beat frequency between the direct and reflected sounds can be amplified and used in earphones to hear the pulse sound.

Doppler Pulse Probe

The pulse of a premature infant may be very difficult to detect with a stethoscope since the sound produced is extremely faint. A sensitive Doppler pulse probe can be used to advantage because it detects the movement of the blood through an artery. The ultrasonic echo from the moving blood can be mixed with the source frequency to produce a beat frequency. As the blood surges with the pumping action of the heart, the beat frequency signal changes in frequency and amplitude.

Remarkably, in clinical Doppler pulse detectors the sound output is similar in nature to what you hear with a stethoscope; you immediately recognize it as a pulse sound.

Heterodyne Principle

Heterodyning is a method for transferring a broadcast signal from its carrier to a fixed local intermediate frequency in the receiver so that most of the receiver does not have to be retuned when you change channels. The interference of any two waves will produce a beat frequency, and this technique provides for the tuning of a radio by forcing it to produce a specific beat frequency called the "intermediate frequency" or IF.

Heterodyne Principle

An electromagnetic carrier wave which is carrying a signal by means of amplitude modulation or frequency modulation can transfer that signal to a carrier of different frequency by means of a process called heterodyning. This transfer is accomplished by mixing the original modulated carrier with a sine wave of another frequency. This process produces a beat frequency equal to the difference between the frequencies, and this difference frequency constitutes a third carrier which will be modulated by the original signal.

Heterodyning is extremely important in radio transmission -- in fact, the development of heterodyning schemes was one of the major developments which led to mass communication by radio. By fixing the beat frequency between the incoming carrier and the local oscillator to a fixed intermediate frequency (IF), most of a radio receiver can be constructed so that it can be used by any incoming radio signal. Only the local oscillator is tuned to produce a beat frequency equal to the fixed IF frequency. We now take for granted that one radio receiver can be tuned to any of the locally broadcast radio stations, but if it were not for heterodyning, you would have to have one receiver for each broadcast station.

AM and FM Radio Frequencies

The Amplitude Modulated (AM radio) carrier frequencies are in the frequency range 535-1605 kHz. Carrier frequencies of 540 to 1600 kHz are assigned at 10 kHz intervals.

The FM radio band is from 88 to 108 MHz between VHF television Channels 6 and 7. The FM stations are assigned center frequencies at 200 kHz separation starting at 88.1 MHz, for a maximum of 100 stations. These FM stations have a 75 kHz maximum deviation from the center frequency, which leaves 25 kHz upper and lower "gaurd bands" to minimize interaction with the adjacent frequency band.

The bandwidth assigned to each FM station is sufficently wide to broadcast high-fidelity, stereo signals. The carrier frequency is directly modulated with the sum of the left and right channel audio signals. A 38 kHz subcarrier also modulates the carrier, and that subcarrier is modulated with the difference, L- R , of the audio signals. The FM tuner then decodes this signal and separates the Left and Right audio channels.

Tuning of music instrument

Musicians commonly use interference beats to accurately check tuning at the unison or other simple harmonic intervals. Piano and organ tuners even use a method involving counting beats, aiming at a particular number for a specific interval.