Many phones have a silent, vibration only mode as part of the regular alarms.
A cheap Fitbit Flex band will do that too.
If a vibrating alarm isn't enough, you can get a wristband that delivers electric shocks to wake up, such as the Pavlok wristband ( store ):
At first, it will act like any other alarm clock, with a gentle vibration to get you up.
But if you keep ignoring the vibration or hitting snooze, the wristband will send a shock to wake you up for good.
For a custom solution : (from Wallace and Gromit )
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You should not feel self conscious about having to wake up early.
We've all had to do this at some point during our (backpacking) travels, hence you can expect people to be tolerant about your early bird alarm.
Having said this there are a few unwritten rules you should respect when having to get up early in the morning in a shared hostel room: Place your alarm next to you so that it is readily available and can be turned off quickly.
Don't place it out of reach (for example stashing is at the bottom of your packed bag is what you shouldn't do) because it will take you ages to get to it before you can turn it off hence ensuring that it'll wake other people up too.
Don't hit the snooze button.
If you have to get up, get up.
One snooze might be acceptable but it would be better to avoid snoozing alltogether.
Don't turn on the light.
If you have to get ready use a flashlight, or your phone for lighting.
If your alarm didn't manage to wake other up, turning on the lights most probably will.
Pack your stuff the night before so that you won't have to spend half an hour rummaging through your pack looking for a clean pair of socks thus waking everyone else up.
This is especially true if you have a tendency of packing your gear in plastic bags.
Indeed these tend to make an unholy amount of noise which appears to be particularly unbearable in the early morning.
If you have en-suite bathroom facilities, shower the night before .
Waking up to the sound of running water might be pleasant if you camp next to a river but not in a hostel room.
Out of sheer courtesy, warn your room-mates about your early-bird alarm .
This will allow them to prepare for it, and take some counter measures to avoid being woken up (including wearing earplugs, sleeping under the pillow, etc.).
Everything goes after 08:00.
This is a sensible unwritten rule I found on this hostel etiquette website which states that the limit for unholiness when it comes to early birds is 08:00 in the morning.
All in all your main objective should be to be as courteous as possible to avoid waking others up too without hindering your right to an early bird start of the day.
For more information on the topic note that the internet is scattered with Hostel Etiquette webpages or blog posts.
I already linked one, here is another interesting one .
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Immediately turn off your alarm after you're awake.
So, keep the alarm very close to your ears, under or next to your cushion, or perhaps above your head, if your hostel bed allows for that.
And find the lowest sound level that wakes you.
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You can also get a vibrating alarm, which you can find in stores selling goods for hearing-impaired people.
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If you fall asleep easily, perhaps you could fall asleep with the earphones (of earbud type) in your ears and have an alarm set up on your phone with the earphones connected to the phone (set up so that the phone's speakers are muted and all sound goes to the earphones).
This can be enhanced by using the tip from the comments on having phone's vibration on.
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Have you tried a sleep cycle alarm clock (e.g. Sleep Cycle by Northcube )?
I too am a heavy sleeper but if it vibrates at a shallow stage of sleep, it could wake you up without any sound.
A much cheaper alternative than the shock wristband.
Perhaps try using the sleep cycle as a primary alarm and the noisy alarm as a back-up if you really want to minimize the chance of waking others.
Also, a free version of the sleep cycle alarm clock is to time your sleep in multiples of 90 minutes--you're most likely to be in a shallow stage of sleep at 90, 180, 270, etc.
minutes after nodding off.
If you set a vibrating alarm for yourself at any of those points, you're likely to wake up with minimal disturbance to neighbors.
I find myself doing this the most these days.
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I'm a pretty heavy sleeper and sometimes I need to wake up earlier for a bus/flight or to catch early light.   When sharing a room in a hostel type place, what's a good way to set an alarm without waking the whole room ?
Most respectful way to set alarm when sharing the room
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You should not feel self conscious about having to wake up early, although you can do your best to wake up and get ready without disturbing others too much. You could pack your stuff and shower the night before, and keep your alarm next to you and set to vibrate or sound over headphones. If a vibrating alarm isn't enough, you can get a wristband that delivers electric shocks to wake up, such as the  Pavlok wristband. Hostel etiquette suggests that when guests have an early start they should try to be as courteous as possible to other people in the same room. Some tips include getting a vibrating alarm or sleeping with earphones in. There are a few unwritten rules like not hitting the snooze button and not turning on the light. Moreover, it is recommended that early birds pack and take a shower the night before, as well as warn room-mates of the early departure.
There are a number of devices that will wake you up without waking other people who are sleeping. These include a vibrating alarm, a wristband that delivers an electric shock and sleeping with earphones in. Waking up early is not a crime. However, courtesy to other people sleeping in the room is important. There are several things you should and should not do when waking up early in a dormitory. You should not hit snooze on the alarm or turn on the light. You should pack the night before, take a shower the night before and turn off your alarm immediately. It is also best to warn your room-mates of your early departure the night before.