Question

10)Write the following statements using symbol of
variation
a) The wavelength of sound (I) and its frequency are in
direct variation
b) The intensity (1) of light varies inversely with the square
of the disance (d) of screen from the lamp.​

Answer 1

Step-by-step explanation:

• When two quantities x and y are in inverse proportion (or vary

inversely) they are written as x ∝ 1

y

. 

• Two quantities x and y are said to be in direct proportion if they

increase or decrease together in such a manner that the ratio of

their corresponding values remains constant. That is, x

y

= k where

k is a positive number, if x and y are in direct proportion or vary

directly. In case of direct proportion, if y1, y2 are the values of y

corresponding to the values x1, x2 of x respectively, then 1 2

1 2

x x

y y  .

• Two quantities x and y are said to be in inverse proportion if an

increase in x causes a proportional decrease in y and vice-versa, in

such a manner that the product of their corresponding values

remains constant. That is, xy = k where k is a positive number, if x

and y are in inverse proportion. In this case, if y1, y2 are the values

of y corresponding to the values x1, x2 of x respectively, then x1 y1=

x2 y2 or

x y

x y

1 1

2 2



• Quantities increasing or decreasing together need not always be

in direct proportion, same in the case of inverse proportion.

• When two quantities x and y are in direct proportion (or vary directly),

they are written as x ∝ y. Symbol “∝” stands for ‘is proportional to’.