One of the things that were very unnatural for me while learning English was the "th" sound. Do all native English speakers actually pronounce it this way or does it vary between accents (Canadian, US, Australian, UK islands)? Does it actually stand out if I pronunce it as "f"?
Learn English – Do all native English speakers actually pronounce the “th” sound
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This is a tricky question, because the answer from a pure phonetic perspective doesn't match the perception of most native English speakers. (Either British or American.)
In the phonological perception of native English speakers, the three allomorphs of the plural -s suffix are /s/, /z/, and /əz/. /z/ occurs after the final /l/ of 'apples', making singular /'æpəl/ into plural /'æpəlz/. As a native speaker of American English, I thought this was the whole story until I studied phonetics. If you ask other native English speakers, they will most likely agree that 'apples' ends with a /z/ sound.
From a pure phonetic perspective, the actual pronunciation of word-final /z/ in English often has very little voicing. This is surprising if you're expecting /z/ to be voiced and /s/ to be unvoiced. Since word-final /z/ may have very little voicing, as an English learner you might mistake it for /s/.
In typical speech, a big phonetic difference between word-final /s/ and /z/ is in the length of the syllable. Syllables ending with /s/ or another unvoiced obstruent are pronounced with a much shorter vowel, compared to syllables ending with /z/. In other words, native English speakers would only perceive a word like 'apples' as ending with /s/ if the pronunciation of the preceding /əl/ were very short.
English has a lot more vowels than most languages, so most learners need to re-train their ears to recognize the additional vowels. In both British English and American English, the difference between ball and bowl is small, but significant. It is easy for native speakers to recognize because their ears are trained to do so.
In ball, the vowel is a long vowel: that means that it sounds the same all the way through. The same long vowel occurs in law- /lɔː/ in BrE and /lɑː/ in AmE.
In bowl, the vowel is a diphthong, which means that there is a glide between two different sounds. The same diphthong occurs in low- /ləʊ/ in BrE and /loʊ/ in AmE.
You can see the difference clearly in this spectrogram of a British English speaker saying ball and bowl. In the first word, ball, the long vowel is the same all the way through. In the second word, bowl, the diphthong sound changes, starting at the red cursor line.
Regarding your comment about casual, fast-paced conversations: when people speak casually, and when they speak quickly, the parts that lose clarity are the function words: the little words that provide the structure for the language.
Take the word and, for example: the strong form is /ænd/, but most of the time we use the weak form /ənd/. As speech gets progressively faster and/or more casual, it becomes /ən/ and finally /n/.
Meanwhile, the important words- nouns like ball and bowl- are usually stressed, and don't soften up in the same way. The central vowel in a stressed word is about as protected as you can get.
You might get some de-stressing if the noun is preceded by an adjective (the red ball) or when it's part of a compound noun (a furball), and this might weaken the clarity a little, but not, in my opinion, enough to make it impossible to discriminate for a native listener with the same accent.
Best Answer
Most native English speakers you hear will effortlessly pronounce the th digraph you're having trouble with. While there are some dialects of English that pronounce it /d/ or /t/ or /f/ depending on position, standard pronunciations in the US and UK pronounce it "normally" and that is what you should strive to emulate if you want to sound like a native speaker.
There are phonemes in every language that non-native speakers have trouble with, and English is no exception. This is the advantage of growing up speaking a language from childhood. And by this I mean from very early childhood, what most people would consider the pre-verbal period of a baby's life.
Some studies have shown that unless a baby hears its language's phonemes in its first six months of life, it may never code for them at all.
The point is, yes, it's hard to duplicate certain sounds in another language. You may never pronounce those sounds perfectly. But unless you make the effort, your pronunciation will always mark you as foreign* and, worse, you may have trouble communicating with native speakers.
Addendum
In response to a comment I'm including further information about the critical nature of language exposure in the early months of life:
It's worth noting that they say babies before their first birthdays are beginning to lose "the ability to hear the distinctions among phoneme in languages other than their own." Not that they've lost it, but that the longer a child goes without hearing those distinctions and, consequently, producing them itself, the harder it will be for that child to reproduce all the language's sounds. By the time one reaches adulthood, it can be a monumental task.
Anecdotally, my own name, which is Germanic and contains the ü sound in German, is extremely difficult for me to pronounce fluently; and a word like Brüder, with its combination of the glottal /r/ immediately followed by the ü, is well-nigh impossible for me—even though I worked in Germany for a time and acquired a fair bit of fluency. It was always a source of chagrin for me, especially when I would hear my coworkers pronounce my name flawlessly and without effort.
* And in case you think that it's all right to use those non-standard sounds produced by dialectical speakers, be aware that even to sound like them you would have to master the whole range of their pronunciations as well, and be able to use those when appropriate, which would be just as big a task (if not bigger) as learning the standard version.