1. The following fourwaves are sent along strings with the same linear densities

Question

1. The following fourwaves are sent along strings with the same linear densities( x
is in meters and t is in seconds). Rank the waves according totheir tensions.
(1) y1 = (3 cm) sin(x 3t)
(2) y2 = (6 cm) sin(2x t)
(3) y3 = (1 cm) sin(4x t)
(4) y4 = (2 cm) sin(x 2t) 2. Consider a ladder ofmass 10 kg and length 4m, leaning against a vertical wall at
an angle of 30o with the vertical. The coefficient of frictionbetween the ladder and the floor
is s = 0.40, and there is no friction between the wall and theladder. A man of mass 80 kg
climbs up the ladder. How high can he climb before the ladderbegins to slip? 1. The following fourwaves are sent along strings with the same linear densities( x
is in meters and t is in seconds). Rank the waves according totheir tensions.
(1) y1 = (3 cm) sin(x 3t)
(2) y2 = (6 cm) sin(2x t)
(3) y3 = (1 cm) sin(4x t)
(4) y4 = (2 cm) sin(x 2t) 2. Consider a ladder ofmass 10 kg and length 4m, leaning against a vertical wall at
an angle of 30o with the vertical. The coefficient of frictionbetween the ladder and the floor
is s = 0.40, and there is no friction between the wall and theladder. A man of mass 80 kg
climbs up the ladder. How high can he climb before the ladderbegins to slip?

Explanation / Answer

1. Since the linear density is same for each, speed isproportional to square root of tension.    y = Asin(kx - wt)     phase speed of wave = /k.       so, tensionsare proportional to :       3, (0.5),(0.25), 2,    clearly, the waves are in the order oftension,    1,4,2,3 2. For two unrelated questions you must post the twoseparately.

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