# Beat Frequency vs. Average Frequency

#### Transformers

10+ Year Member
If there are two waves (100 HZ + 200HZ), I am confused about beat frequency and average frequency. If you hear the average frequency (150HZ), then what exactly is the beat frequency of 100Hz (f1-f2)?

Thanks.

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#### wanderer

10+ Year Member
5+ Year Member
If there are two waves (100 HZ + 200HZ), I am confused about beat frequency and average frequency. If you hear the average frequency (250HZ), then what exactly is the beat frequency of 100Hz (f1-f2)?

Thanks.
Do you have a source that indicates that one hears the average frequency?
If you were to simultaneously hit the two keys on a keyboard that correspond to the notes of 100 and 200 Hz they would not sound anything like the note that corresponds to 150 (I'm assuming the 250 is a typo). Maybe if the two notes were very close (like 200 and 199 Hz) it would sound like the average.

#### thebillsfan

##### Unseasoned Veteran
10+ Year Member
5+ Year Member
Do you have a source that indicates that one hears the average frequency?
If you were to simultaneously hit the two keys on a keyboard that correspond to the notes of 100 and 200 Hz they would not sound anything like the note that corresponds to 150 (I'm assuming the 250 is a typo). Maybe if the two notes were very close (like 200 and 199 Hz) it would sound like the average.
wanderer, i actually have read somewhere in my mcat materials something (cant remember where or what) that implied that yes, you do hear the average frequency. i'm not sure if that applies only to "very close" notes (intuition says it does) but if someone could verify/refute this that would be good.

#### Transformers

10+ Year Member
Correct me if im wrong, but BEAT FREQUENCY applies to the frequency of the amplitude oscillations of the resulting frequency....so a 100Hz and 200Hz (of constant amplitudes but that are slightly out of phase) will produce a wave with a frequency of 150 Hz, whose amplitude variations (and thus intensity and loudness variations) have a beat frequency of 100Hz.

#### wanderer

10+ Year Member
5+ Year Member
Correct me if im wrong, but BEAT FREQUENCY applies to the frequency of the amplitude oscillations of the resulting frequency....so a 100Hz and 200Hz (of constant amplitudes but that are slightly out of phase) will produce a wave with a frequency of 150 Hz, whose amplitude variations (and thus intensity and loudness variations) have a beat frequency of 100Hz.
Incorrect. The resulting sine wave has a frequency which is 100 Hz (I used this applet: http://www.udel.edu/idsardi/sinewave/sinewave.html ), and beat frequency is only used when the two waves are somewhat close in frequency.

Do you have any musical instruments lying around anywhere?

#### kentavr

10+ Year Member
Incorrect. The resulting sine wave has a frequency which is 100 Hz (I used this applet: http://www.udel.edu/idsardi/sinewave/sinewave.html ), and beat frequency is only used when the two waves are somewhat close in frequency.

Do you have any musical instruments lying around anywhere?
Hmmm. Is that on MCAT?

The beat frequency I guess can be derive like this
sin(at) + sin(bt) = 2* sin((at+bt)/2)cos((at-bt)/2) (trig identity)

so when a~b then cos is close to 1
and approximate result of the sum is sin(a+b)/2 (or average of two freqs). That will be the main harmonic.

Second, I lied that cos is close to 1. It is just much slower cosine. It modulate the amplitude of fast sine and this modulation will be interpreted as a second sound with frequency a-b. (I guess this is the beat)

If A not close to B then graph will be much harder to interpret as two sounds (main and beat)

#### Transformers

10+ Year Member
i mean guys, basically i wanna distinguish between what the frequency of the RESULTING wave is and what you hear?

...i mean lets say you have two isntruments playing at 99 and 101 Hz...do you hear 2 Hz or 100Hz...?

#### wanderer

10+ Year Member
5+ Year Member
i mean guys, basically i wanna distinguish between what the frequency of the RESULTING wave is and what you hear?

...i mean lets say you have two isntruments playing at 99 and 101 Hz...do you hear 2 Hz or 100Hz...?
Aprrox. 100 Hz, but the cycle within the cycle so to speak (that is the oscillation of amplitude) is 2 Hz. So every half second the cycle repeats, but the pitch will sound like the pitch of a 100 Hz sound.

#### pandoraaj009

10+ Year Member
You definitely heard from the EK physics book, pg 103/104 about average freq vs beat frequency (from here on out, I'm just gonna call this the beat). here's a summary of that, plus some stuff I've picked up from other sources (waves/sound was my weakness; I've accumulated quite a lot of stuff on it):
(I looked @ (berkley review physics book 2, pg 38, question 16).

*PITCH= FREQUENCY=LOUDNESS=AVERAGE FREQUENCY I prefer think of pitch as loudness, as well as freq, for a more intuitive way to remember it. Think of the range for hearing; it's always given in Hz So anyways, EK phy pg 104 gives a scenario of tuning a piano with a tuning fork. The person listens to the beat. For perfect tuning, the beat is zero.

"What the person actually hears is the pitch. The freq creating the pitch would be an average of freq's from the piano and the tuning fork. Pitch correlates with freq, a high note has high freq and pitch."
what the person hears when tuning instrument. beat is alternating increase and decrease in intensity.

Pg 103: beat frequency is when 2 waves with slightly different freq's are superimposed. @ some pts, there's constructive interference, and destructive @ other pts.

Those points alternate with the beat= absolute value of f1-f2

I mean, we all know that formula.

Summary:
Constructive and destructive interference between 2 waves create sounds with intensities that cycle from loud to quiet.
*What do we hear? pitch=average of 2 frequencies.
*beat=variation of intensity=difference in frequency between 2 waves.