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:
$\lambda= \frac{v}{f} = \frac{343.06 m/s}{293.66 Hz}=1.168 m$

Converting into centimeters, we have:
$\lambda= 1.168 m =1.168 \cdot 10^2 cm =116.8 cm$