you should write 演武(they are both 3rd tone)

but you should read  演( 2nd tone)武( 3rd tone)

it  occurs when two  3rd tone be together.

延(2nd)误(4th)：write and read in the same way 

Is your question does a word like the 請 in 請你 sound different to a word like 晴天？

Does a second tone sound different to a tone that is being changed to a second tone? 

The answer is no, they sound completely the same. 

Laurence

1.演(ㄧㄢˇ) 3rd

    武(ㄨˇ)3rd

2.延(ㄧㄢˊ)2nd

   誤(ㄨˋ) 4th

演武：the tone goes from 2nd to 3rd

延误：the tone goes from 2nd to 4th