Sound 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 they 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 audio-induced electromagnetic radiations (EMRs) from mobile devices' audio circuits can be exploited as an effective side channel in recovering the victim's audio sounds. Our theoretical analysis and feasibility studies further reveal that audio-induced 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 to clear 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 12 mobile devices and 6 headphones. The recovery results are recognizable to natural human hearing and online speech-to-text tools. We also propose a software-based defense solution that mitigates this audio eavesdropping threat without requiring hardware modification.