Answer
$v=3.43m/s$
Work Step by Step
To find the frequency of the sound according to the moving observer, the Doppler effect equation must be used, which is $$f'=f(\frac{v \pm v_o}{v \mp v_s})$$ where $v$ is the speed of sound, $v_o$ is the speed of the observer, and $v_s$ is the speed of the other sound. Since the observer is moving closer to a sound, a higher frequency will be heard. To find the frequency, remember that $$f_{beat}=|f_2-f_1|$$ Therefore, if the beat frequency is $4$ Hz and the sound must be higher to the observer, the frequency is $404$ Hz. This means that $$404Hz=(400Hz)(\frac{343m/s+v_s}{343m/s})$$ Solving for $v_s$ gives $$343m/s+v_s=346.43m/s$$ $$v_s=3.43m/s$$
