Sympathetic string vibration plays an essential role in the clavichord's sound quality and tonal identity. Sympathetic vibration comes from the undamped string segments between the bridge and tuning pins. Under some conditions, a specific note, a whistling tone, stands out of the reverberation halo due to sympathetic vibration. It is hypothesized that this whistling tone comes from resonance between played and sympathetic segments of strings that are coupled through the bridge. Vibratory measurements for three pairs of excited and sympathetic strings are conducted on a copy of a historical instrument by Hubert (1784). The influences of bridge mobility and tuning on sympathetic string frequency and damping are studied. The results show a significant increase in vibratory amplitude, frequency veering and damping increase of the string segments when tuning approaches frequency coincidence. Numerical simulations of a reduced clavichord model corresponding to the experiments are conducted using the modal Udwadia-Kalaba formulation. Simulation gives a more accurate picture of the veering phenomenon. Simulation and experimental results are in good agreement, showing that whistling in the clavichord comes from string resonance. It is favored by frequency coincidence between excited and sympathetic string segments and by higher bridge mobility.