3. For a vibrating string of length 5' With xEd ends. Bh mode 9f vibration can be written as a: maa, t} = My; Sin(mkt + "3ij sini: f3") where wk = kg\" and Mg, m are determined by initial conditions. For all k 3.:- 11 sin{"':" 1'] has zeros in [0, f], at say points 3: = 2;, so uz, t} = {l for all t. Points where the deection u of a mode is zero [Meat] = U] are called nodes. {at} What is the distance between nodes for each mode it 3:: 1? {b} 1Where should you place your nger so that it is at a node of the second mode? This will prevent an},? mode that doesn't have a node at this point, such as the rst mode, from vibrating. Express your answer in terms of fraction of the distance from the bridge, so that an answer 1 would be an open string, I] would be no string at all. {c} 1Where should you place your nger so that it is at a node of the third mode? This will prevent an}.r mode that doesn't have a node at this point1 such as the rst and second modes, From vibrating. Again give your distance in terms of a fraction of the distance from the bridge