Find the frequency in terms of the reference frequency of a sound which haa a pitch of 360 cents.

To find the frequency in terms of the reference frequency, we need to understand what "cents" means in relation to pitch.

In music theory, the term "cents" is used to quantify the difference in pitch between two sounds. It is a logarithmic scale where 100 cents represent one semitone in Western music. Therefore, 12 semitones make up an octave, which corresponds to 1200 cents.

To find the frequency ratio for a given number of cents (n), we use the formula:

Frequency Ratio = 2^(n/1200)

In this case, the number of cents is 360. Let's substitute it into the formula:

Frequency Ratio = 2^(360/1200)

Using a calculator, we can evaluate the expression:

Frequency Ratio ≈ 2^(0.3) ≈ 1.231

The frequency ratio represents how many times the original frequency needs to be multiplied to get the desired pitch. For example, a frequency ratio of 1.231 means that the new frequency will be 1.231 times greater than the original frequency.

If we have the reference frequency, we can multiply it by the frequency ratio to obtain the new frequency:

New Frequency = Reference Frequency * Frequency Ratio

Note: The reference frequency could be any value you choose as the starting point for your calculations.