I'm using the Form Maker plugin to handle a form on my wordpress website. This plugin works for this project because it allows for all sent forms to be seen and filterable on the backend as well as be able to send the info to an external database.
For a form that has already been created using the Form Maker plugin (see here [url removed, login to view]) a new field needs to be added which gives the user the hability to record audio and attach it to the form. This audio can then be also seen/played on the backend as with the other information on the form.
There are many voice recording plugins available, anyone can be used or a custom development as long as it is working 100% with this plugin.