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Q. 50

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 485

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Short Answer

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = r fn for all n. In this system, the frequency doubles every 12notes—an interval called an octave.

a. What is the value of r?

b. Orchestras tune to the note A, which has a frequency of440 Hz. What is the frequency of the next note of the scale (called A-sharp)?

a) The value of the r is 1.0595

b) The frequency of the next scale note is 466 Hz

See the step by step solution

Step by Step Solution

Step 1: Discussion about the frequency of the note 

The higher and the lower frequencies waves are responsible for oscillating the higher and lower notes.

Step 2: Understanding the differences between the notes and determining r

The provided information is

the separation of the two notes are

Thus, the separation of the 12th notes are

The double of the twelve-note is

based on the simplifaction the remaining value is

Now the r is =

Thus, the determination of the r based on the formula is

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