Use the Swiss army knife for sound generation, SoX.

You install it from the official repositories, simply by typing:

sudo apt-get install sox

Updated, fancy answer (pleasing ocean waves):

After experimenting a bit with SoX, I came up with this great command which imitates the soft murmur of the sea with its soothing sound of waves that flow over a flat sandy beach on a sunny summer day...

Well, enough poetry, here's the command. Listen yourself.

play -n synth brownnoise synth pinknoise mix synth sine amod 0.3 10

Explanation:

This command first generates and mixes brown noise and pink noise, which I find to be the most comfortable and natural noise. Then it generates a sine wave of 0.3 Hz with an offset of 10% and uses this to modulate the amplitude of our mixed noises to produce the sound of ocean waves.

Modifications:

• Timer:
  You can add a timer and limit the playback duration by specifying the number of seconds, the number of minutes and seconds (mm:ss) or the number of hours, minutes and seconds (hh:mm:ss) right before brownnoise. Here's an example for one hour:

  play -n synth 1:0:0 brownnoise synth pinknoise mix synth sine amod 0.3 10
  

• Wave frequency:
  If you want the waves to hit the beach more or less frequent, simply change the frequency of the sine wave used for amplitude modification (0.3 in the above command). The number represents the amount of waves per second, so a frequency of 0.1 Hz will cause 0.1 waves per second and therefore make one wave last for 10 seconds:

  play -n synth brownnoise synth pinknoise mix synth sine amod 0.1 10
  

• Minimum background noise volume:
  The sine that is used for amplitude modulation got shifted to an offset of 10%, so the brown-pink noise will always be played with at least 10% volume. If you want a stronger or weaker background noise, increase or decrease this offset to your needs. Here's an example with 20% background noise:

  play -n synth brownnoise synth pinknoise mix synth sine amod 0.3 20
  

Old, boring answer (plain white noise):

Now the easiest command to play white noise infinitely (until you abort it with Ctrl+C) is this:

play -n synth whitenoise

If you prefer a time limit, you may add that in the format hh:mm:ss. The following command would make noise for one and a half hour, for example:

play -n synth 01:30:00 whitenoise

It even shows you some nice stats while "playing":

$ play -n synth 00:00:05 whitenoise 

  Encoding: n/a           
  Channels: 1 @ 32-bit   
Samplerate: 48000Hz      
Replaygain: off         
  Duration: unknown      

In:0.00% 00:00:05.12 [00:00:00.00] Out:240k  [!=====|=====!] Hd:0.0 Clip:0    
Done.

You can generate pink noise using the play command from the sox utilities:

sudo apt-get install sox
play -t sl -r48000 -c2 -n synth -1 pinknoise .1 60

Adjust the values of .1 and 60 to suit your needs. Pink noise is less harsh on the ear and is hopefully the sound you require

Not sure that this will produce real white noise that covers the whole spectrum, but a simple

pacat /dev/urandom

seems to do the trick on my system (no need to install anything new or add a repository).

I'm a glutton for punishment, so I'll give you the GUI way. Take a look at ANoise.

The default sound that it comes with is bad, but you can download other sounds like Forest Rain, Fountain, & Others. You can set it to start with the system, and even set it to stop after a certain time.

sudo add-apt-repository ppa:costales/anoise
sudo apt-get update
sudo apt-get install anoise

ANoise Code, And for For extra river sound:

sudo apt-get install anoise-community-extension1

Open Audacity.

Go into "Generate > Noise..."

Select "Brownian" (way less aggressive than actual white noise). Amplitude and duration does not matter much.

Loop using Shift+Play button.

FFMpeg has an audio noise source filter. You can play it using ffplay:

ffplay -f lavfi -showmode 0 -i 'anoisesrc=color=brown'

The arg to -i is interpreted as a lavfi filter graph, because of -f lavfi. -showmode 0 disables ffplay's default audio visualizer window, which it shows by default for audio-only inputs.

As you can see from the output of ffmpeg -h filter=anoisesrc, you get a choice of brown/pink/white noise at whatever amplitude and samplerate you like, optionally with a finite duration.

You can also use mpv, a nice fork of mplayer, or other players that allow ffmpeg filtergraphs. e.g.

mpv  av://lavfi:anoisesrc=color=brown

This might be handy if you have a custom audio-output setup configured for your favourite player.

The installed-by-default utility speaker-test generates pink noise (which, as @nightingale, is what you really want, not white noise). It can be set to do so indefinitely by running

speaker-test -l 0

I see that nobody has used aplay yet so try the following:

aplay --channels=2 --format=S16_LE --rate=44100 --duration=3600 /dev/urandom

It is not terribly imaginative so I have added in a timer to compensate :). The duration settings is in seconds so this will run for 1 hour and then turn off, hopefully the baby will have settled by then...

Tom Swiss of unreasonable.org uses the following code (using sox) to generate white/pink noise. You'll need to first install sox (sudo apt install sox), then create a shell script with the following code:

#!/bin/sh

len='7:00:00'

if [ "$1" != '' ]; then
  len=$1
fi

play -t sl - synth $len  pinknoise band -n 1200 200 tremolo 20 .1 < /dev/zero

Hat tip http://unreasonable.org/white_noise_generator_with_sox_for_Linux

Disclaimer: I have not tried this myself yet

White noise is mathematically an even distribution of frequencies. You can produce it with random data from /dev/random or /dev/urandom. If you want to change the "tone" of the produced noise (for example to make it less "weighty" by removing lower frequencies, or to make it "damper" by removing higher frequencies) then you could use a command such as dd bs=1 if=/dev/urandom of=whitenoise.raw count=1048576 to generate some white noise, then import it into Audacity and use the high-pass and low-pass filters to adjust it to your liking (when using the filters remember that the average human ear will hear frequencies up to 20kHz).

EDIT: Audacity can also generate white noise itself.