Some dictionaries mark the pitch (OS X built-in, 三省堂スーパー大辞林).
はし ［0］ 【端】
はし ［1］ 【箸】
はし ［2］ 【橋】
The number marks which mora the pitch changes on.
Here’s some visualisations (the final empty dot denotes the pitch of a following particle は, に etc)
[Edit: as regards the OP’s question, 人工 and 人口 are both [0], so they would sound the same and context would be the determiner - or the speaker might choose different words to avoid misinterpretation!]
Bad example. Thats actually a classic example of pitch accent so those words DO sound different and you dont need context LOL.
It would be good for you to look into pitch accent paterns. Most of the time, words that japanese learners think are pronounced the EXACT SAME WAY, actually have different pitch accent paterns. If a japanese person can’t undertand a specific word you’re saying, try changing the accent patern and it might make the difference.
I realized minutes later that I didn’t really mean “pronunciation” as much as I meant that the words share the same syllables (は & し). But, I figured I’d leave it, as the guys after me gave really detailed clarifications. applause
I figured lol. I thought it was weird that you used a classic example for pitch accent differences and then made it sound like they shared the same pitch accent.
I’m a dummy but not THAT much of a dummy. I AM a level 7 after all. 
In actual usage there are still lots of context helpers, chopsticks would probably be referred to as お箸, and bridge would likely have the name of the bridge first 丸子橋, . 人工 would likely precede another noun 人工(の)N whereas 人口 would likely follow N(の)人口.
Since no-one seems to have mentioned it yet, I’ll link to the WaniKani Pitch Info userscript, one of the best userscripts for WaniKani, it will show the correct pitch accent along with the words meaning when you learn it (or when you look up the vocab’s page on WaniKani).
I wondered too, given such a specific example LOL. I just know it’s given me headaches to find out so late in the game, so if I can save one person that headache you can bet I’ll do just that!
Hahaha, I was all-in on it wasn’t I? 
I realized it quickly after, but yours and @Subversity’s responses were so good that I left mine in there as reference. I completely agree @ the headaches it’s caused, and hopefully this thread as whole will save the OP from making this mistake. I’ll take the hit on this one as the poor example lol. Thanks again!
Only problem with that is it freezes on the review page. At least with firefox 57 and tampermonkey.
Homophones are the number one thing that pisses me off about learning Japanese. With a syllabary / alphabet that has over twice as many characters English, the vast majority of which include both a consonant and a vowel, it should be very easy to eliminate all homophones within the restrictions of the syllabary.
Instead, they have an absurd number of homophones.
Why?
WHYYYYYYYYYYYY?!?!
I’ve complained about it on the forums before. Some people said that the written Chinese that was adopted for Japanese was never even intended to be spoken aloud. It was meant to purely be read.
That sounds like the perfect time to go “citation needed.” Because there’s absolutely zero evidence of that.
Anyway, in reality, even words that still have the same pitch accent are rarely going to cause problems. It’d take a sentence like はははははる（母は歯張る) to create a serious issue. Just like in English, “The night the knight went out to meet the meat bear he couldn’t bear it so instead red a read book.” doesn’t present a serious issue. It’s the same way in Japanese. You’ll have far bigger issues with confusing words like 思う and 申す
Ah that sucks. Works fine for me in Safari 11 on macOS Sierra.
For a workaround you should be able to edit the @include's of the script. To do this, just open the file up for editing (go to Tampermonkey dashboard and click the edit button next to Wanikani Pitch Info), and change the following lines at the start:
// @include https://www.wanikani.com/*
// @include http://www.wanikani.com/*
To:
// @include *://www.wanikani.com/vocabulary/*
// @include *://www.wanikani.com/lesson/session
That just makes it so it only loads on the vocabulary and lesson pages, and not the review page.
Despite having more characters than English, they actually still have fewer phonemes. We have something like twenty vowel sounds, for instance, compared to the Japanese five, and twenty-four consonants compared to ~seventeen in Japanese. And even though we have all these extra sounds to play with, we still have a shitload of homophones (as @Syphus so ably demonstrated) so it’s to be expected that Japanese has as many and more (barring pitch accent).
As for me, not going into the debate about pronounciation cuz i’ve only just started, what my japanese teacher told us in class was that if there were a doubt about a word and it’s homophones, the speaker would just ‘‘write’’ it off in his hand, with his finger. So the 人工-vs-人口 would be really easy to figure out.
Or else for complicated kanji, they would say ‘‘人口 : 人のじんと口のこう’’ -> ''じん from the kanji person (said ひと), the こう from the kanji mouth (said くち) ‘’. Generaly using an other kanji pronounciation, if it was on’yomi than in kun’yomi and vice versa.
But English needs a mix of consonants and vowels, so the way you can combine characters is far more restrictive. bcd isn’t a word. jrl isn’t. You have to mix consonants and vowels. Also, the vast majority of words are three or more characters long.
Japanese, on the other hand, can combine literally any character with any other character. Pretty much the only exception is that a word can’t start with a singular “n”. Also, in contrast to English, any singular phoneme can have meaning. There is no lower limit to the amount of characters you need to actually make a word, again, with the exception of “n”.
So, even though Japanese has less phonemes, the syllabary is structured in a way that should allow for little to no homonyms, due to the flexibility of arranging characters. Instead, the opposite is true, and Japanese seems to have far more homonyms than any other language I’ve encountered.
ん seems to be used as a morpheme on it’s own (as a contraction of の) sometimes. Pretty casual, but see http://jisho.org/search/んだ for an example.
You need at least a vowel in both languages in order to make a word, or have you forgotten that with one exception all Japanese syllables end on a vowel sound?
As for “combining literally any character” … Rendaku, chiisai tsu…? There are exceptions (just as there are in English too) but there still exist rules for how sounds in Japanese generally go together.
Beyond that, you can’t arrange phonemes in Japanese any way you want. You can’t put two consonants together, for example, other than ん.
The lower limit for phonemes in a word in English is also one. “A” and “I” are just two examples.
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