If you need help sleeping or just like to have a little sound in the background while you work or exercise, these apps will get the job done.
The first, White Noise (4.5/5 stars, all ages, currently FREE) is today’s Amazon’s Free App of the Day. From Amazon:
Recommended by Dr. Oz as a miracle for better sleep! Features ambient sounds of the environment like ocean waves, rain storms, flowing streams, and more. 
Includes 40+ perfectly looped ambient sounds, audio background service so you can use other apps, and an advanced alarm and timer system that wakes you up refreshed. Featured in Health Magazine, The Washington Post, New York Times, PC Magazine, and raved about by thousands of satisfied customers. Find out why the world is sleeping better with White Noise.
Includes the following great features:
– 40+ perfectly looped sounds for relaxing or sleeping.
– Import new sounds for free from the White Noise Market at http://whitenoisemarket.com/
– Background audio support so you can use other apps – Designed to work on all Android-based phones and tablets
– Create multiple alarms that slowly fade in, waking you up feeling refreshed
– Sleep digital LED clock perfect for any nightstand. Drag up and down to adjust brightness. Swipe left and right to adjust color.
– Sound timers turn off audio to save battery life and fade audio out so [you] won’t suddenly awaken
– Star your favorite sounds in the catalog for quick access in the favorites category view
– On-screen media and volume controls and gesture support allows swiping left or right to navigate sound collection
– Tons of custom settings: Device volume, sound volume, balance, buffer size, auto play, background audio, headset unplugged, auto sleep clock, prevent clock burn-in, allow screen lock, auto share on sleep, prevent device interruptions, alarm snooze time, changelog, help tips, rate app, restore defaults, and send feedback
– No Ads
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Those who’d like a step up in this type of app will want to check out Relax Melodies Premium: A White Noise Ambience For Sleep, Meditation & Yoga (4.5/5 stars, all ages, currently priced at $2.99). This app not only provides pre-recorded sounds and music, but allows you to mix various tracks together to create your own, custom track to provide yourself with a personalized soundtrack for relaxation or falling asleep. From Amazon:
Relax Melodies Premium, the leader in personalized relaxation and sleep assistance, is now available for your Android Phone! No more insomnia for you, tension is a thing of the past at any moment! Just custom mix your favorite high quality sounds from a selection of 94, then slip naturally into a relaxed state or a deep, rejuvenating sleep. This is the ultimate relaxation experience and it’s super easy to use!
Get the most personalized relaxation experience it’s possible to have. With just a few taps, you can create the exact MELODY that resonates perfectly with you. With ambient and binaural selections, you can choose whether to simply relax or tell your brain that it’s time for sleep. It can even help your baby fall asleep faster!
– Sound background support. Relax while using other apps!
– Mix your favourite sounds together with different volume to create your own personal melodies
– 94 High quality ambient sounds including 6 binaural beat frequencies for brainwave entrainment.
– Timer system to stop the melodies when you go to sleep
– Individual sound volume adjustment
– Save, name and replay your favorite mixes easily
– Complete and easy to follow help screen
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Alarm Clock Xtreme (4.5/5 stars, all ages, currently priced at $1.99) is an app for those who don’t have trouble getting to sleep, so much as getting out of bed in the morning. From Amazon:
Wake Up
Have you ever shrugged off your alarm clock, turning it off only to fall back asleep? Wake up gently and avoid accidentally disabling your alarm with Alarm Clock Xtreme. This alarm clock includes features that prevent excessive snoozing and get you out of bed so you can get a productive start to the day. Alarm Clock Xtreme can even automatically disable itself when it detects that you’re traveling to work or school using GPS (requires the GPS plugin available for free in the Amazon Appstore).
Conscious Calculations
Choose an unlimited number of alarms, set alarms to repeat, and let your music wake you up with a random song option. Set your morning alert to slowly increase the volume and wake you up in a soothing manner. Force yourself to do math in order to snooze or set the shake to snooze option. The snooze button is extra large, and you can even set a maximum number of snoozes.
Full Featured
This alarm clock includes the following features: unlimited alarms, repeating alarms, music alarm, random song alarm, gentle alarm volume ramp up, math to snooze/disable, shake to snooze/disable, minimum speed to disable, nap alarm with countdown timer, large snooze button, snooze 1-60 min, decrease snooze duration after each snooze, max number snoozes, auto-snooze, auto-dismiss, option to keep screen locked keeping the phone safe in your pocket, and analog alarm clock widget.
Do not install Alarm Clock Xtreme to the SD Card. The app will be unable to re-start automatically when the phone reboots or the SD Card is mounted/unmounted. This will cause you to miss alarms. Phone must be on for alarm to work.
Note that those who use this on a Kindle Fire must ensure their Fire is not fully shut down (e.g., do not press and hold the power button and tap the Shut Down button) when they want to use the app. So long as your Fire is only ‘sleeping’ (e.g., you’ve only closed your Fire HD’s cover or have lightly pressed the power button once), the app will ‘wake’ your Fire when it’s time for an alarm. Users may want to set their usual alarm clock the first time they use this app, or test it on a weekend, to ensure they’ve got all the settings right.
About using this app on a Kindle Fire specifically, one reviewer says:
The alarm settings are great, choose from sounds or music, limit your snooze settings so you never over-snooze, set for weekdays only so you are not disturbed during the weekend. The timer has saved me also.
Fire users need not worry. I ran into the problem where the alarm would not turn off and it was due to my display being set to never sleep. When I turned the screen sleep function back on to 30 minutes, the alarm worked properly again. I have found no other problem with using this app of my Fire, and the app has been on/functioning for months now, I never turn the alarm app off.
Another reviewer says:
I have not overslept once since downloading. I am someone who sets their alarm up to an hour earlier than I need to, just so I can hit snooze enough times to actually wake up. I never thought I’d like the feature of a math problem being required to be answered correctly before the alarm stops, but I love that I have not over slept by even five minutes since I started using it. You can also set for up to 3 equations to be solved before it disables if you are somewhat of a sound sleeper. I NEVER pay for applications, but I will always be happy that I bought this.