Beats occur when two sounds of different frequencies reach the ear. The interference of the waves causes the overall sound to rise and fall in amplitude at a rate equal to the difference between the frequencies. If two waves have frequencies of 330Hz and 350Hz, the beat frequency will be 20Hz, which is the absolute value of the difference between the frequencies. When tightening a piano string from 448Hz to 450Hz, the beat frequency remained 2Hz, so the original frequency must have been 448Hz. For a tuning fork at 430Hz sounding with a guitar where 10 beats occurred in 3 seconds, the guitar's frequency is either 433.33Hz or 426.67Hz.

1. Beats
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2. What is ‘Beats’
• ‘Beats’ are formed when two waves with different
frequency approaches your ear.
• The sounds constructive and destructive interference
causes the sound to be alternatively soft and loud.

3. Beats formula
• The number of beats per second is equal to
the difference in frequency.
•

4. Beats
• Beats are created from the interference of two waves
that are very close to each other, creating a higher and
smaller amplitude in different region.
• Beat Period is define by the distance between the two
maximum amplitudes.

5. General Formula
• Fb = Beat Frequency
• F1 and F2 = Two sound frequency
• |F1 – F2| = Absolute value (Always postive)

6. Example
• If there are two waves with frequency of
330Hz and 350Hz.
– The resulting frequency will be the average of the
two waves. (330+350)/2 = 340 Hz
– The beat frequency will equal to Fb =|F1 – F2|,
therefore Fb = |330-350| = 20 Hz

7. Question 1
• If your tuning your piano, and you tighten the
piano spring to 450 Hz. You notice that the
beats of 2 Hz remains the same. What was the
frequency of the piano note before you
tighten the string.

8. Answer
• Fb =|F1 – F2|
• Fb = 450 Hz – 2
= 448 Hz
*When the string is tighten, the velocity and
frequency of the waves must have increased.

9. Question 2
• A tuning fork with a frequency of 430 Hz
sound together with a note played on a guitar,
10 beats are recorded in 3 seconds. What is
the frequency of the guitar note?

10. Answer
• Fb =|F1 – F2|
• Find the beats frequency
– 10 Beats / 3 sec = 3.33
• Then apply the formula
– 3.33 Hz = |430 Hz – F2|
– = 433.33 Hz or 426.67 Hz
– * This is because of the absolute sign ‘||’ the
answer will always be positive, thus two answers.