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Audio eavesdropping poses serious threats to user privacy in daily mobile usage scenarios such as phone calls, voice messaging, and confidential meetings. Headphones are thus favored by mobile users as it provide physical sound isolation to protect audio privacy. However, our paper presents the first proof-of-concept system, Periscope, that demonstrates the vulnerabilities of headphone-plugged mobile devices. The system shows that unintentionally leaked electromagnetic radiations (EMR) from mobile devices' audio amplifiers can be exploited as an effective side-channel in recovering victim's audio sounds. Additionally, plugged headphones act as antennas that enhance the EMR strengths, making them easily measurable at long distances. Our feasibility studies and hardware analysis further reveal that EMRs are highly correlated with the device's audio inputs but suffer from signal distortions and ambient noises, making recovering audio sounds extremely challenging. To address this challenge, we develop signal processing techniques with a spectrogram clustering scheme that clears noises and distortions, enabling EMRs to be converted back to audio sounds. Our attack prototype, comparable in size to hidden voice recorders, successfully recovers victims' private audio sounds with a word error rate (WER) as low as 7.44% across 11 mobile devices and 6 headphones. The recovery results are recognizable to natural human hearing and online speech-to-text tools, and the system is robust against a wide range of attack scenario changes. We also reported the Periscope to 6 leading mobile manufacturers.