Two ropes are joined smoothly to form a single rope, which is attached to a wall. If the ends of the two ropes are moved up and down in phase, but one rope is half a wavelength longer than the other to the point where they join, will the interference of the two waves when they join be constructive or destructive?

Let's first understand the principle of superposition states that when two or more waves combine, the resulting disturbance or displacement is equal to the sum of the individual displacements.

Thus, Wave length in the one rope is half wave length longer than the other to the point where they join. So, at this point waves are out of phase. Hence the interference of the waves when they join is the DESTRUCTIVE

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

cant without the picture! ?