A string composed of two segments of different linear density joined just in the middle of the string is held at a tension of 30 N. When a speaker near the string maintains a frequency of 200 Hz, it is observed that a standing wave is formed in the chord so that one segment has 2 loops and the other 3 loops, with a node in the center of the compound chord.

1. Show that the relationship between the linear densities of segments 1 and 2 is given by (14 p):

2 = 2.25 1

2. The total length of the composite chord is 1 m, calculate the linear mass densities of both segments (8 p).

3. Calculate the total mass of the compound string (6 p).

4. The speaker increases the frequency to 400 Hz and a standing wave with a node in the center of the composite string is observed again. How many loops are in segments 1 and 2 in this case? (12 p)