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The American R sound is a challenge to master and in my lesson I mention how important the position of your tongue is to getting this right. To make things more difficult, there are words such as "world" which combine the "r" and "l" in words like: world, girl, twirl. So my big tip is to try to say the words were + old and slowly put the two together: were...old, were..old, wereold, world.
We have many vowel sounds in English and this one requires a that you tighten your lips and pull your tongue back. This sound is very important when pronouncing words like, afternoon, soon, school and tool.
Words using the "ah" sound like in "bought" and the "uh" sound in "but" are somewhat similar. However, the "uh" sound is very short. In my lesson you can see from the pictures above that the "ah" sound uses a very relaxed tongue position while "uh" uses a slightly higher, middle-of-the-mouth tongue position.
So these two sounds are spelled as "oo" in many words but one sounds like boot and the other like book. It is very common for people to have difficulty saying the second sound: book. I really suggest you watch this part my lesson if this sound is difficult for you or even if you need to review it.