Given: - Frequency of the electromagnetic wave: \( f = 60 \, \text{MHz} = 60 \times 10^6 \, \text{Hz} \) - Speed of light in air: \( c = 3 \times 10^8 \, \text{m/s} \)
The wavelength \( \lambda \) of an electromagnetic wave is given by the formula:
\[ \lambda = \frac{c}{f} \]
Substituting the given values:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{60 \times 10^6 \, \text{Hz}} \]
Simplifying:
\[ \lambda = \frac{3 \times 10^8}{60 \times 10^6} \, \text{m} \] \[ \lambda = \frac{3}{60} \times 10^2 \, \text{m} \] \[ \lambda = 5 \, \text{m} \]
The wavelength of the electromagnetic wave is \( 5 \, \text{m} \).
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32