A vibrating tuning fork of frequency 512 Hz is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound (resonance) is heard at specific water levels. Assume you start with the tube full of water, and begin steadily lowering the water level. What is the water level (as measured from the top of the tube) for the third such resonance?

Explanation:

This is an example of resonance of air column with one end closed.

For third resonance , length of water column

= 5  x λ / 4

λ ( wave length ) = velocity / frequency

343 / 512

= .67 m

= 67 cm

length of air column

= 5 x λ / 4

= 5/4 x 67 cm

= 83.75 cm

water level will be 83.75 cm below.

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.