I decided to go study Ph.D. in the United States. Is it necessary that my wife be good at English?
I am expressly interested in legal and statutory requirements of English proficiency for a spouse if I am going to be studying in the United States.
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If you are in a large city or at a large university, then it probably isn't necessary. You will probably find a lot of people there, and their spouses, who speak your language, whatever it is.
In a small town, however, it would be a different story, and your spouse might be a bit isolated without some language skills.
There are many large State Universities throughout the country that have students and faculty from all around the world. When I was in grad school in such a place (long ago) I had neighbors from Iran, in fact. Some such large places have organizations for spouses of foreign faculty and students in which people can get together, though everyone tends to speak a different language.
Also, many places, even small ones, have programs in secondary (and other) schools for English as a Second Language (ESL). These are taught by specialists. So, I think that no matter where you are, there would be opportunities to learn even if you didn't find people who speak your own language.
As for the legalities, there is no requirement that a person be able to speak English. However, to become a citizen you need some minimal proficiency: http://pjclaw.net/uscitizenship/english-language-requirements-for-naturalization/. But you don't need proficiency on arrival and, since the process is long, there is an opportunity to learn.
For the requirements to get a visa, see this site: http://www.ustraveldocs.com. But I note that there is no information there about Iran. The best place to get information is to visit a US consulate or similar place where visas are issued and get current requirements.
Disclaimer: I have not done a lot of work with immigration law, especially for education purpose visas.
Presumably you are obtaining an F-1 visa for your program. Your wife will also need to go through a very similar process I believe. She must also enroll in the Student and Exchange Visitor Information System (SEVIS), obtain a separate Form I-20s from your SEVP-approved school, and apply for an F-1 visa. Only you will need to pay the SEVIS fee I believe.
None of these visa applications require direct English proficiency. (Forms may be in English, but she is not required to fill out those forms without assistance). You and your wife will need to pass visa interviews. This is often done in your home country (or a country you have travel access to). Because the interview is done "locally" at the US embassy or consulate, it can be done in a language you can speak. English is not necessary.
Your specific school could give you more guidance on the details of the process.