Question

The pitch of a musical note varies inversely as its wavelength. If a tone has a pitch of 440 vibrations per second and a wavelength of 2.4 feet, find the pitch of a tone that has a wavelength of 1.6 feet

Answer 1

Correct Answer:

660 vibrations

Answer 2

To solve this problem you must apply the proccedure shown below:

1. First, you must calculate the constant of proportionality
`k`. You have that the pitch of a musical note varies inversely as its wavelength, therefore:

`pitch=(k)/(wavelenght) \\ 440=(k)/(2.4)`

2. Now, solve for
`k`:

`k=(440)(2.4)=1056`

3. If the pitch of a tone that has a wavelength of
`1.6 feet`, you must substitute the values of the constant of proportionality and this value of the wavelenght into the equation shown above:

`pitch=(1056)/(1.6)\\ pitch=660 vibrations`

The answer is:
`660 vibrations`