Resolução halliday cap. 17 vol 2 ed. 8

Chapter 17

1. (a) When the speed is constant, we have v = d/t where v = 343 m/s is assumed. Therefore, with t = 15/2 s being the time for sound to travel to the far wall we obtain d = (343 m/s) ( (15/2 s) which yields a distance of 2.6 km.

(b) Just as the [pic]factor in part (a) was 1/(n + 1) for n = 1 reflection, so also can we write

[pic]

for multiple reflections (with d in meters). For d = 25.7 m, we find n = 199 [pic].

2. The time it takes for a soldier in the rear end of the column to switch from the left to the right foot to stride forward is t = 1 min/120 = 1/120 min = 0.50 s. This is also the time for the sound of the music to reach from the musicians (who are in the front) to the rear end of the column. Thus the length of the column is

[pic]

3. (a) The time for the sound to travel from the kicker to a spectator is given by d/v, where d is the distance and v is the speed of sound. The time for light to travel the same distance is given by d/c, where c is the speed of light. The delay between seeing and hearing the kick is Δt = (d/v) – (d/c). The speed of light is so much greater than the speed of sound that the delay can be approximated by Δt = d/v. This means d = v Δt. The distance from the kicker to spectator A is

dA = v ΔtA = (343 m/s)(0.23 s) = 79 m.

(b) The distance from the kicker to spectator B is dB = v ΔtB = (343 m/s)(0.12 s) = 41 m.

(c) Lines from the kicker to each spectator and from one spectator to the other form a right triangle with the line joining the spectators as the hypotenuse, so the distance between the spectators is

[pic].

4. The density of oxygen gas is

[pic]
From [pic] we find

[pic]

5. Let tf be the time for the stone to fall to the water and ts be the time for the sound of the splash to travel from the water to the top of the well. Then, the total time elapsed from dropping the stone to hearing the splash is t = tf + ts. If d is the depth of the well, then the kinematics of free fall