Understanding the main drivers of behavioural disturbance in deep-diving cetaceans would improve predictions of anthropogenic noise effects on individual animals, habitats and populations. To investigate the potential roles of received level and source distance on behavioural disturbance, we tagged 14 sperm whales in northern Norway with multi-sensor data loggers and conducted dose-escalation experiments. Each experiment included 1 to 4 tagged individuals and involved multiple vessel passes ('exposure sessions', n = 25 total) by a navy frigate or research vessel towing a naval sonar, at different starting distances and maximum source levels. We analysed behaviour state series and proxies for locomotor activity and foraging success with generalized additive mixed models. The probability of occurrence of non-foraging active behaviour was affected by received level, source distance and session order, with decreased foraging effort at higher received levels and shorter distances, and during subsequent sessions (indicating short-term sensitisation). Prey capture attempts decreased with increasing received level when whales kept foraging. Similar to what has been suggested for some populations of blue whales and beaked whales regularly exposed to navy sonar, but unlike northern bottlenose whales in more pristine waters, source distance affected sperm whale behavioural responses on a high-latitude foraging ground.