Top tier firms do inform candidates when they are not going forward with their recruitment process. This is done via an ‘automatic’ email notification if in the pre-interview phase (timing can vary by firm and time of the year – when HR are busy it will take longer to screen your application) and generally via phone (with a quick feedback) if in the case interview phase.
Smaller firms/boutiques tend to have less structured/organized processes so that their response can take longer or never arrive:) .
In any case, if you still haven’t heard from them after a while you can always follow up with the HR team (but always remember to act professionally and never sound ‘desperate’ :)).
As an additional comment, applying to 40 firms at the same time seems like a big number to me. My recommendation would be to try to be selective at the beginning and target only those firms at the top of your list: submitting a strong application and networking with your target firm can take a lot of time. Hence is better to focus your effort on a limited selection of firms (this will result in a better preparation). If your top list does not work out, you can later expand list to your top 2 and later top 3 preferences.
Best of luck,