Question

Suppose the Opera station broadcasts at 90.5MHz and the Rock and Roll station broadcasts at 107.1MHz. 1. Which station's signal has waves with longer waveslength? 2. Which station's signal has waves with higher energy?

Answer 1

1).  The "Opera" at 90.5 MHz has lower frequency,
so its wavelength is longer.

2).  Whichever station is transmitting with higher power
has waves with higher energy.

Each photon of the transmission at 107.1 MHz carries more energy,
because the energy of a photon is proportional to its frequency.
But it's a mistake to think that the station at higher frequency has
waves with higher energy.

Answer 2

The longer wavelength and which has higher energy is required.

$90.5\ \text{MHz}$ has a longer wavelength.

$107.1\ \text{MHz}$ has higher energy.

The given frequencies are

$f_1=90.5\ \text{MHz}$

$f_2=107.1\ \text{MHz}$

$c$ = Speed of light = $3\times 10^8\ \text{m/s}$

The wavelengths are

$\lambda_1=\dfrac{c}{f_1}\\\Rightarrow \lambda_1=\dfrac{3\times 10^8}{90.5\times 10^6}\\\Rightarrow \lambda_1=3.31\ \text{m}$

$\lambda_2=\dfrac{3\times 10^8}{107.1\times 10^6}\\\Rightarrow \lambda_2=2.8\ \text{m}$

Energy of a wave is given by

$E=hf$

where,

$h$ = Planck's constant = $6.626\times 10^{-34}\ \text{Js}$

$f$ = Frequency

This means higher the frequency, higher the energy of the wave

So, $107.1\ \text{MHz}$ has higher energy.

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