What would the wavelength be in this Doppler effect example?

Not at all, because you completely ignored the Doppler Effect. Since here observer is stationary, sound velocity, being a property of the medium would remain $340 frac{text{m}}{text{s}}$. However, by the time the wave covers the distance of $1$ wavelength, the source has also moved, causing the $mathbf {effective}$ wavelength to become shorter than what would have been had the source been stationary. Mathematically: $$lambda^prime = lambda - vT$$ where $v$ is source velocity and $T$ is time period. This means that: $$f_{text{app}} = frac{c}{c-v} f$$ Here $c$ is sound velocity, and $f$ is original frequency.