To tackle this problem, let's recall that when one quantity varies inversely with another, their product is a constant. Here, the frequency (f) of the musical note varies inversely with its wavelength (I). This means that [tex]\( f \times I \)[/tex] is constant.
Given:
- Frequency [tex]\( f \)[/tex] = 440 Hz
- Wavelength [tex]\( I \)[/tex] = 2.4 feet
We will denote the constant as [tex]\( k \)[/tex]. According to the inverse variation relationship:
[tex]\[ f \times I = k \][/tex]
Now, substitute the given values for [tex]\( f \)[/tex] and [tex]\( I \)[/tex]:
[tex]\[ 440 \times 2.4 = k \][/tex]
When we calculate [tex]\( k \)[/tex], we get:
[tex]\[ k = 1056.0 \][/tex]
Thus, the constant [tex]\( k \)[/tex] is 1056.0.
Finally, we can write the equation that represents the relationship between the frequency and wavelength:
[tex]\[ f = \frac{1056}{I} \][/tex]
where [tex]\( f \)[/tex] is the frequency in Hertz and [tex]\( I \)[/tex] is the wavelength in feet.
