A string 1.30 meters in length is oscillating in its first harmonic. The frequency of oscillation is 7.80 Hz. What is the wavelength of the first harmonic?

2.6m

Explanation:

The formula for calculating the wavelength is expressed as;

λ = v/f

v is the velocity

f is the frequency of vibration

Given

f = 7.80Hz

We need to get the velocity

For string;

f = V/2L

7.80 = V/2(1.3)

7.80 = V/2.6

V = 2.6 * 7.8

V = 20.28m/s

Get the required wavelength

λ = v/f

λ = 20.28/7.80

λ = 2.6m

Hence  the wavelength of the first harmonic is 2.6m

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.