You can set a custom sound for Pulsate sound notifications in your app. All you have to do is add the sound to your project.
When you've prepared the file, just add it to your XCode project resources, so it ends up in the application bundle. The easiest way is to drag & drop the file and XCode will do the rest.
Custom alert sounds are played by the iOS system-sound facility, so they must be in one of the following audio data formats:
Linear PCM
MA4 (IMA/ADPCM)
µLaw
aLaw
You can package the audio data in an aiff, wav, or caf file.
Custom sounds must be under 30 seconds when played.
Read more in the Apple Documentation
You can add multiple custom push sounds to your app. When you are sending configuring the push notification on Pulsate, click on Advanced Options and switch on Notification Sound. You can then enter the name of any of the audio files that you added to your app project and that audio file will be played when a user received that push notification.
Push Notification Sound