Question

A musical instrument has a pitch of 220 hertz when the wavelength is 3 feet. When the wavelength is 4 feet, the pitch is 165 hertz. What is the type of variation between pitch and wavelength? What is the pitch when the wavelength is 5 feet? hertz

Answer 1

we know that
Inverse Variation is a relationship between two variables in which the product is a constant
so

let
x------> a pitch of a musical instrument
y------> the wavelength
x*y=k

find the value of k
for x=220 hertz   y=3 ft
x*y=k
220*3=k
k=660

for x=165 hertz   y=4 ft
x*y=k
165*4=660
k=660

the answer part a) is
the type of variation between pitch and wavelength is an inverse variation

part b) What is the pitch when the wavelength is 5 feet?
x=?
y=5 ft
k=660
x*y=k------> solve for x
x=k/y----------> x=660/5-----> x=132 hertz

the answer Part b) is
132 hertz