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So recently I have been studying A.C. circuits and the graphs show that the current oscillates itself as a function of time. Now, according to me an oscillating body vibrates. Hence, the oscillating electric current should also make the medium oscillate in which it is flowing. Am I correct in my assumption, if not then why?

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Hold a power cord in between the poles of relatively strong magnet and you'll feel it vibrate. – M. Enns 14 hours ago
    
So, have I made correct assumption.? – Vaibhav Singh 14 hours ago
2  
You are correct in as much as some charges in the body are vibrating but the mass of the moving charges in an AC circuit are tiny compared to the mass of the conductor. Consider the mass of a single electron compared to a copper atom. In an external magnetic field the moving charges experience a Lorentz force that can be strong enough to make the whole conductor vibrate. – M. Enns 14 hours ago
    
Now that opened my sense more.. – Vaibhav Singh 14 hours ago
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Oscillating does not always mean vibrating. Oscillation simply means some measurable value is cycling back and forth. This could be a vibration, which would be a measurable change in position, back and forth (like a grandfather clock or your phone's vibrator), but oscillation is a more general concept. For example, in linguistics, we talk of oscillation in linguistic patterns which seem to go back and forth, back and forth. There's no physical movement in that case, but there's still an oscillation.

AC does not automatically mean vibrating. It's merely the fact that the measurable current is oscillating between forwards and backwards. Technically, electrons are moving, but you'll find its a very tiny effect.

However, you will find things operating on AC do in fact vibrate. This is due to second order effects. The changing current can cause changing magnetic fields, which can draw components together and push them apart in tune with the AC oscillations. This is the source of the humming you will hear from many devices.

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The jargon for the last effect is "magnetostriction". – Eric Towers 5 hours ago
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Some components such as resistors, capacitors, and semiconductors aren't very prone to vibration. Other components like transformers are and have to be constructed to prevent audible vibrations. Back when CRTs were very common, it was not unusual for the coil(s) in their flyback transformer to loosen over time and cause a high-pitched noise. It could be downright annoying for those who could hear it.

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She same with the starter in fluorescent lights. Viz. the practical joke in Gympl / The Can – Jan Dvorak 54 mins ago

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