I think there is some mode with phone such as no-sound, vibration, or sound. How can I express this mode on natural way. When phone-rings alarm. I didn't expect I make any interrupting someone. I totally forgot to change sound mode to silence How can I say it? In this situation, I should have a silence mode to sound mode
Most commonly people will say that the phone is "muted" or the phone is "on mute" to indicate that the speaker and vibrator will not alert you. So, you may hear one say that you should "mute your phone" or that my phone is "muted". However, in some contexts (e.g. movie theater announcements before the main feature) they will suggest that you "silence your phone". Also, some phones have a "silent" mode instead of a mute mode.
The answer above works, saying the phone is "on mute", or "silent", but many people also say "my phone is on vibrate" to express the same idea. To say what you are asking about, you could must say, "I'm sorry, I forgot to turn off my phone's sound/put it on vibrate/change it to silent", etc. As a native English speaker, I would most likely say "put it on vibrate".