Sound generation by nanosecond repetitively pulsed plasma discharges is investigated experimentally. High voltage pulses of 10 nanosecond duration provide rapid heating of the air. A high-frequency pulse train between 20 and 30 kHz is burst modulated to generate low-frequency components. The generation of pressure waves from the modulated discharge pulse train is characterized based on acoustic measurements in an impedance tube. Different combinations of modulation frequency, electrode gap distance, modulation duty cycle and pulse repetition frequency are studied in terms of electric energy and acoustic source amplitude. The measurement results suggest that overall, the amplitude of the pressure wave components at the modulation frequency can be well estimated based on the electrical power using an analytical expression for acoustically compact unsteady heating. As an application of sound generation by low-frequency modulated NRP discharges, feedback control is applied to suppress thermoacoustic instabilities in a Rijke tube. The pressure oscillation amplitude is reduced by more than two orders of magnitude when the plasma discharges are suitably synchronized with the self-excited fluctuations.