Answer to Question #165717 in Optics for jays

Question

Suppose you are located 180 m from a radio transmitter.What if this station is 98.1 FM? (The FM band frequencies are in megahertz.)

Answer 1

Radio waves are the electromagnetic waves, so the velocity of the radio waves is $3\times 10^{8}m/s$ .

The frequency of $98.1FM$  band (in megahertz) is $98.1 \times 10^6 Hz$ .

Now, Substitute  $98.1\times10^6 Hz$ for $f$  and $3.0 \times10^8 m/s$  for $v$ in the equation $\lambda = \dfrac{v}{f}$

$\lambda= \dfrac{3.0\times10^8m/s}{98.1\times10^6Hz}=3.058m$

Now, Substitute 3.058m for $\lambda$ in the equation, $n\lambda=180$ m

$\because$ $n\lambda = 180$

So, $n= \dfrac{180}{\lambda}$

$= \dfrac{180}{3.058}\ =58.56$

Round off to the three significant digits,

$n=58.9$

Hence, the number of wavelengths present between radio station and you are 58.9 or 60(approx.)