Key points A popular conception of mammalian cochlear physiology is that tuned mechanical vibration of the basilar membrane defines the frequency response of the innervating auditory nerve fibres However, the data supporting these concepts come from vibratory measurements at cochlear locations tuned to high frequencies (>7 kHz). Here, we measured the travelling wave in regions of the guinea pig cochlea that respond to low frequencies (<2 kHz) and found that mechanical tuning was broad and did not match auditory nerve tuning characteristics. Non‐linear amplification of the travelling wave functioned over a broad frequency range and did not substantially sharpen frequency tuning. Thus, the neural encoding of low‐frequency sounds, which includes most of the information conveyed by human speech, is not principally determined by basilar membrane mechanics. Abstract The popular notion of mammalian cochlear function is that auditory nerves are tuned to respond best to different sound frequencies because basilar membrane vibration is mechanically tuned to different frequencies along its length. However, this concept has only been demonstrated in regions of the cochlea tuned to frequencies >7 kHz, not in regions sensitive to lower frequencies where human speech is encoded. Here, we overcame historical technical limitations and non‐invasively measured sound‐induced vibrations at four locations distributed over the apical two turns of the guinea pig cochlea. In turn 3, the responses demonstrated low‐pass filter characteristics. In turn 2, the responses were low‐pass‐like, in that they occasionally did have a slight peak near the corner frequency. The corner frequencies of the responses were tonotopically tuned and ranged from 384 to 668 Hz. Non‐linear gain, or amplification of the vibrations in response to low‐intensity stimuli, was found both below and above the corner frequencies. Post mortem, cochlear gain disappeared. The non‐linear gain was typically 10–30 dB and was broad‐band rather than sharply tuned. However, the gain did reach nearly 50 dB in turn 2 for higher stimulus frequencies, nearly the amount of gain found in basal cochlear regions. Thus, our data prove that mechanical responses do not match neural responses and that cochlear amplification does not appreciably sharpen frequency tuning for cochlear regions that respond to frequencies <2 kHz. These data indicate that the non‐linear processing of sound performed by the guinea pig cochlea varies substantially between the cochlear apex and base.