Measuring vocal-tract acoustics is one key issue for singing voice characterization. We aim at developing a non-invasive experimental tool that would assess the singer's vocal-tract acoustical behavior during singing. Grounded on previous impedance measurements, a broadband external acoustic source (chirp signal) loads vocal tract at the lips while phonating. Both chirp and voice signals are recorded by a microphone. An open-mouth condition measurement calibrated by a closed-mouth condition provides vocal-tract frequency response, from which resonance frequencies and quality factors can be estimated. A challenging aspect is to separate voice from chirp signal. We propose a new method for signal separation and test it numerically. Its applicability to real singing is then explored on vowels sung by a modern-style singer. First step consists in estimating voice fundamental frequency on recorded voice+chirp signal. Secondly, an informed high-order chirplet analysis is performed on this signal to eliminate voice, recovering only modulated chirp. Numerical simulations, based on synthesizing vowel [a] sung at 450Hz while adding a 3dB-lower chirp, show that the method is accurate enough for resonance frequencies (resp. quality factors) not to deviate by less than 3 cents (resp. 5%). The method is applied on recordings of a modern singer and singing teacher. The subject was asked to sing vowel [a] with different voice qualities and for several pitches (F3, G3, A3). Measurement was done during a one-second sustained phonation (voice condition) and during a following closed-glottis condition with instruction to keep vocal tract in same position (silence condition). Voice condition forces to apply voice-chirp separation method, on contrary to silence condition. Results show that the closed-glottis instruction causes additional vocal tract adjustments, even for a trained singer. The differences in resonances between registers are explored as a function of pitch and voice quality.