A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe

(a) it is a closed pipe

(b) the fundamental frequency, is 88 Hz.

Explanation:

Given overtones;

The overtones for open pipes are given as;

The overtones for closed pipes are given as;

Where;

is the fundamental frequency

(a) From the given overtones;

test for open pipe;

396 Hz ≠ 440 Hz (it is not open pipe)

Test for closed pipe;

(b) the fundamental frequency, is 88 Hz.

unlike poles attract

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.