The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments

Force is 161.27 N and frequency of vibration when the string vibrates in three segments is 660 Hz .

Explanation:

Given :

Frequency , f = 220 Hz .

Length of wire , L = 70 cm = 0.7 m .

Mass of wire ,

a ) We know, frequency in string is :

Therefore ,

   .... equation 1.

Here , is mass per unit length .

So,

Putting value of in equation 1.

We get ,

b) We know , frequency of when n segment are in string :

For , n = 3

Hence , this is the required solution.

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.