Can I use their sound in my app?
Is there any way I can use their sound and not violate copyright?
If the sound is available from the copyright holder under a free or open source license (likely a Creative Commons license, for a sound file), or if the work is in the public domain (e.g., copyright on the work has expired), then you may use it in your app, provided you follow any requirements imposed by the license on the work (at minimum, this will include showing a license notice and showing original authorship information in your app). You can check if the app you want to borrow from has a "credits" screen that might contain licensing information.
Otherwise: because the sounds are covered by copyright, using them without a license from the copyright holder would be a copyright violation. Doing so makes you liable for copyright infringement.