Question

to calculate the frequency of a note on a piano in the same octave or a different octave, the hertz (hz) of a particular note can be multiplied by the ratio of change in the octave between the original note and the new note to indicate the hz. when not starting at c major for an octave, the ratio would need to be calculated using a formula. for example, moving from d to b on the same octave would be done with a ratio derived from: $\frac{b}{d}=\frac{\frac{15}{8}}{\frac{9}{8}}=\frac{15}{9}=\frac{5}{3}$. thus, a note at d would be a different hz value on the same octave at b based on the ratio multiplier as indicated above between the notes on the same octave as follows: $\frac{5}{3}=\frac{b}{300}$. what would the hz be at b if the d note is 300 hz (convert to an equivalent fraction)?

Explanation:

Step1: Identify the proportion equation

We have the proportion $\frac{5}{3}=\frac{B}{300}$, where $B$ is the frequency of note $B$ and 300 is the frequency of note $D$.

Step2: Cross - multiply

Cross - multiplying gives us $5\times300 = 3\times B$.
So, $1500=3B$.

Step3: Solve for $B$

Dividing both sides of the equation $1500 = 3B$ by 3, we get $B=\frac{1500}{3}=500$.

Answer:

$500$