Beats

Discussion

introduction

Text!



A beat pattern at two different scales.

Text.

x = A sin 2π(ƒ1t) + A sin 2π(ƒ2t)  
 
x = 2A sin 2π
ƒ1 + ƒ2  t
 cos 2π
ƒ1 − ƒ2  t
2 2

Beats are interference in time. (Fringes are interference in space.)

dtmf

The phrase "Touch Tone" was originally a registered trademark of the American Telephone and Telegraph company, but is now public domain. Source: USPTO.

In the Touch Tone telephone dialing system, pairs of tones are used to represent the digits 0 through 9 and the symbols * (star or asterisk) and # (pound, number, hash, or octothorp). The tones assigned correspond to the location of the button on a standard keypad. The row determines the low tone and the column the high tone. The numeral 5, for example, lies on the keypad row and column that plays 770 Hz and 1336 Hz, respectively. The full set of eight frequencies were chosen to avoid harmonics (no frequency is a multiple of another) and beats (no frequency is the difference between two frequencies). While it is possible to use a touch tone keypad as a musical instrument, the touch tone frequencies do not correspond to the notes of any known musical scale. The pairs of tones together produce a sound that is quite unique and unlikely to be generated by accident.

 
1209 Hz
1336 Hz
1477 Hz
1633 Hz
 
697 Hz
 
1
 
 
2
ABC
 
3
DEF
 
A
FO
 
770 Hz
 
4
GHI
 
5
JKL
 
6
MNO
 
B
F
 
852 Hz
 
7
PRS
 
8
TUV
 
9
WXY
 
C
I
 
941 Hz
 
 
 
0
OPER
 
#
 
 
D
P
 
  complete dtmf (touch tone) keypad  

The A, B, C, D tones were originally a part of the US military's Autovon phone system. While the Autovon system has been disbanded, some non telephone applications use still use these tones.

  1. Flash Override (FO)
  2. Flash (F)
  3. Immediate (I)
  4. Priority (P)

The Touch Tone system is an example of a signaling technique known as dual tone multi frequency (DTMF). Next example: telephone event tones.


Spectral analysis of a dial tone (US). Note the peaks at 350 and 440 Hz. The two tones together beat at 90 Hz, which sounds something like a ringing phone.

event frequency (Hz) duration (s)
low high on off
 
 
busy signal
 
 
480 620 0.5 0.5
 
 
congestion
 
 
480 620 0.25 0.25
 
 
dial tone
 
 
350 440 continuous
off hook warning
1400
2060
2450
2600
0.1 0.1
 
 
ringback
 
 
440 480 2.0 4.0
 
 
ringback (japan)
 
 
384 416 1 2
ringback (uk)
400 450 0.4
0.4
0.2
2.0
Telephone Event Tones (US except where indicated)

Why do phones ring?

ebs

The Emergency Broadcast System was a broadcast protocol in effect in the United States from 1963-1997. It has since been replaced with the Emergency Alert System. Radio and television stations across the nation were required to transmit a special audio signal whenever the local or national authorities needed to alert the general population of an emergency situation. Although designed to warn of a military attack, the system was normally used to warn of natural emergencies like tornadoes or flash floods. The EBS system is most famous, however, for its frequent tests. These consisted of the EBS alert tone followed by an announcement that the sound you just heard was only a test. ("Had this been a real emergency ….") The EBS alert tone is actually two tones of similar pitch that form a particularly spooky beat frequency. Since the EBS was a Cold War civil defense initiative many people associate this tone with the approach of nuclear attack and the end of the world.

This is a test. This station is conducting a test of the Emergency Broadcast System. This is only a test.

ebs alert tone

 
[flow = 853 Hz, fhigh = 960 Hz, ∆t = 22.5 s]

This is a test of the Emergency Broadcast System. This station, in voluntary cooperation with federal, state, and local authorities, has developed this system to keep you informed in the event of an emergency. Had this been an actual emergency, the attention signal you just heard would have been followed by official information, news, or instructions.

This concludes this test of the Emergency Broadcast System.

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