humming noise when starting the car in cold

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Hi, About 3 month ago, i had my service and mechanic suggested to change tires. Sometimes i get the squeaking and humming noise when making turns in downhill. Recently I hear humming noise when starting the car, especially in cold. If I move steering wheel left to right, the humming noise varies, but this noise disappears after 5-10 minutes of driving I am planing to change tires, but was wondering if there is anything else I should be looking at