A sound damping device includes a sound damper and a support member. The sound damper includes a contact surface configured to contact a vibration member and includes a through-hole having a first opening formed on the contact surface. The support member is coupled to the sound damper to support the sound damper and cause the vibration member and the contact surface to come into contact with each other. The support member includes an air hole that is connected to the through-hole of the sound damper and that penetrates through the support member.