Question

a certain stretched string has a frequency of 250Hz , what is the new frequency if one (a) increase the tension by a factor of 4 while keeping everything else constant (B) increase the length by a factor of 3 while everything else constant (c) increase the mass / length by a factor of 2 while everything is constant (d) decrease the diameter by a factor of 2 whiles everything else constant

Answer 1

a)

frequency in a stretched string is given as ::

f = frequency

L = length of the string

T = tension in the string

m = mass per unit length

as we can see from the formula , f is propotional to squareroot of tension T

hence as tension is made 4 times , frequency becomes 2 times

so new frequency = 250 x 2 = 500 Hz

b)

from the above formula , frequency "f" is inversly propotional to length "L"

so if we make length 3 times , the frequency will become 1/3 rd

so new frequency = 250/3 = 83.3 Hz

c)

from the above formula , frequency "f" is inversly propotional to squareroot of mass per unit length "m"

as "m" is made 2 times , "f" becomes 1/sqrt(2) times

so new frequency = 250/sqrt(2) = 177.3 Hz

d)

as diameter is decreased, frequency will not change