Beats

The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged

prev | up | next

Discussion

introduction

Text!



A beat pattern at two different scales.

Text.

equation

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: US Patent & Trademark Office.

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.

Touch Tone Frequency Pairs
low tones high tones
  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

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.

Telephone Event Tones (US except where indicated)
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 (UK)

400 450 0.4
0.4		 0.2
2.0
ringback (Japan)

384 416 1 2

Why do phones ring?


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.

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.

EBS Frequency Pairs
event frequency (Hz) duration (s)
low high
ebs alert tone 853 960 22.5

additional topics

Summary

Problems

practice

  1. A 32.83 ms fragment of the EBS alert tone is shown in the oscilloscope display below. (The full tone lasts 22.5 seconds.) The beat structure is plainly visible at this scale. There are approximately 3.5 cycles of the beat and 29.75 cycles of the carrier visible in the display window. Determine the frequencies of the two tones used to produce the alert.



    Solution …
    • Start by determining the beat and carrier frquencies from the information given in the description.
               
      ƒbeat =  3.5  /  0.03283 s  = 107 Hz
      ƒcarrier =  29.75  /  0.03283 s  = 906 Hz
               
      Then work backward to determine the two source frequencies.
                     
      ƒbeat =  ƒ1 − ƒ2  = 107 Hz   ƒ1 − ƒ2  = 107 Hz   ƒ1 = 960 Hz
                     
      ƒcarrier =  ƒ1 + ƒ2  = 906 Hz   ƒ1 + ƒ2  = 1812 Hz   ƒ2 = 853 Hz
      2  
              2ƒ1  = 1919 Hz    
                     
      These are indeed the values specified by the Federal Communications Commission.
  2. Write something else.
    • Answer it.
  3. Write something different.
    • Answer it.
  4. Write something completely different.
    • Answer it.

numerical

  1. The telephone "off the hook" warning in the United States is composed of four pure tones: 1400, 2060, 2450, and 2600 Hz.
    1. How many beat frequencies are present in this combination?
    2. What are the beat frequencies?

Resources

prev | up | next

Another quality webpage by

Glenn Elert		 eglobe logo home | contact

bent | chaos | eworld | facts | physics