Question

the frequency of a stringed instrument is inversely proportional to the string length. if an instrument produces 527 hertz frequency with a string length of 42 cm, then what the frequency be for 67 string length in cm?
hint: remember an inverse proportion means the ratio of either frequencies or string lengths needs be reversed or inverted.
$y = \frac{k}{x}$ where $y$ can represent the hertz and $x$ can represent the string, while $k$ is a constant.
the frequency is in hertz, but you do not need to use a label for your answer. you only need to enter the number. round to the nearest tenth if necessary.

Explanation:

Step1: Find the constant \( k \)

Given \( y = 527\) (frequency) and \( x = 42\) (string length). Using the formula \( y=\frac{k}{x}\), we can find \( k\) by \( k = y\times x\).
So, \( k=527\times42\)
\( k = 22134\)

Step2: Calculate the new frequency

Now, we have \( x = 67\) and \( k = 22134\). Using the formula \( y=\frac{k}{x}\), substitute the values:
\( y=\frac{22134}{67}\)
\( y\approx330.4\)

Answer:

\(330.4\)