Suppose you sound a 1056-hertz tuning fork at the same time you strike a note on the piano and hear 2 beats/second. You tighten the piano string very slightly and now hear 3 beats/second. What is the frequency of the piano string?

The frequency of the piano string is either 1053 HZ or 1059 HZ.

Explanation:

Here we know that frequency of beats is equal to the difference between the frequencies between two waves .

     Given that frequency of tuning fork is 1056 HZ  .

     Let the frequency of the piano be ' f ' .

   Given that number of beats = 3.

    We know that   | 1056 - f | = 3 ;

                      ⇒       1056- f = ±3,

         Upon solving this we get  

                        f = 1056-3 and 1056 + 3

                   ⇒ f = 1053 or 1059 .

b

explanation:

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.