Method for operating an acoustic measuring apparatus, in which - at least one sound measurement transducer of the acoustic measuring apparatus is provided, wherein the at least one sound measurement transducer is designed to transmit and/or receive sound signals, - an output signal from the at least one sound measurement transducer is delivered and an echo signal of the output signal from the at least one sound measurement transducer is received, - a time characteristic of the echo signal is recorded, - the time characteristic of the echo signal is used to determine a first estimate (T_sig_1) of a delay in the sound signal from the beginning of the output signal to the beginning of the echo signal, - a cross-correlation between the echo signal and a reference sinusoidal signal is used to ascertain a characteristic of a cross-correlation function on the basis of a frequency and a phase of the reference sinusoidal signal, wherein the frequency of the reference sinusoidal signal is varied such that it is in a prescribed range around a frequency of the output signal, - a value (f_0) of the frequency of the reference sinusoidal signal and a value (phi_0) of the phase of the reference sinusoidal signal for which a maximum value of the cross-correlation function is achieved are ascertained, and - the value (f 0) of the frequency of the reference sinusoidal signal and the value (phi_0) of the phase of the reference sinusoidal signal for which the maximum value of the cross-correlation function is achieved and the first estimate (T_sig_1) of the delay in the sound signal from the beginning of the output signal to the beginning of the echo signal are taken as a basis for determining an updated estimate (T_sig_2) of the delay in the sound signal from the beginning of the output signal to the beginning of the echo signal. - at least one sound measurement transducer of the acoustic measuring apparatus is provided, wherein the at least one sound measurement transducer is designed to transmit and/or receive sound signals, - an output signal from the at least one sound measurement transducer is delivered and an echo signal of the output signal from the at least one sound measurement transducer is received, - a time characteristic of the echo signal is recorded, - the time characteristic of the echo signal is used to determine a first estimate (T_sig_1) of a delay in the sound signal from the beginning of the output signal to the beginning of the echo signal, - a cross-correlation between the echo signal and a reference sinusoidal signal is used to ascertain a characteristic of a cross-correlation function on the basis of a frequency and a phase of the reference sinusoidal signal, wherein the frequency of the reference sinusoidal signal is varied such that it is in a prescribed range around a frequency of the output signal, - a value (f_0) of the frequency of the reference sinusoidal signal and a value (phi_0) of the phase of the reference sinusoidal signal for which a maximum value of the cross-correlation function is achieved are ascertained, and - the value (f 0) of the frequency of the reference sinusoidal signal and the value (phi_0) of the phase of the reference sinusoidal signal for which the maximum value of the cross-correlation function is achieved and the first estimate (T_sig_1) of the delay in the sound signal from the beginning of the output signal to the beginning of the echo signal are taken as a basis for determining an updated estimate (T_sig_2) of the delay in the sound signal from the beginning of the output signal to the beginning of the echo signal.