Question

The frequency of the middle d note on a piano is 293.66 hz. what is the wavelength of this note in centimeters? the speed of sound in air is 343.06 m/s.

Answer 1

The relationship between speed, frequency and wavelength of a wave is:

`v=\lambda f`
where v is the speed,
`\lambda` the wavelength and f the frequency.

In our problem, the frequency of the middle d note is f=293.66 Hz, while the speed of the wave (which is a sound wave) is v=343.06 m/s. Using the previous relationship, we can find the wavelength:

`\lambda= (v)/(f) = (343.06 m/s)/(293.66 Hz)=1.168 m`

Converting into centimeters, we have:

`\lambda= 1.168 m =1.168 \cdot 10^2 cm =116.8 cm`