the no of wave in 6cm of vacum is same as that of no of wave in xcm of medium is 3/2 find the value of x
To find the value of x, we can set up an equation using the given information.
Let's assume that the number of waves in 6 cm of vacuum is represented by n, and the number of waves in x cm of a medium is represented by m.
According to the given information, the number of waves in the vacuum is the same as 3/2 times the number of waves in the medium:
n = (3/2)m
We know that the speed of light is constant in a vacuum and in a medium, so the wavelength of the waves can be used to calculate the number of waves.
The wavelength (λ) is given by the equation λ = c/f, where c is the speed of light and f is the frequency of the waves. Assuming the frequency is the same in vacuum and the medium, we can write:
λv = cv/f
λm = cm/f
Since the number of waves is equal to the length divided by the wavelength, we can write:
nv = 6/λv
nm = x/λm
Substituting the values from the wavelength equations into the number of waves equations, we get:
nv = 6/(cv/f)
nm = x/(cm/f)
Simplifying these equations:
nv = 6f/c
nm = xf/c
Since the number of waves in the vacuum is equal to 3/2 times the number of waves in the medium, we can write:
6f/c = (3/2)(xf/c)
Simplifying this equation:
6f = (3/2)xf
Now, we can cancel out the frequencies (f) from both sides:
6 = (3/2)x
Finally, solving for x:
x = (6*2)/3
x = 12/3
x = 4
Therefore, the value of x is 4.