Beats

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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.

Beats formula

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

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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.

General Formula

• Fb = Beat Frequency

• F1 and F2 = Two sound frequency

• |F1 – F2| = Absolute value (Always postive)

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

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.

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.

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?

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.