Question

problem#1:
a radio wave has a wavelength of 3 meters. what is its frequency?
v = λf
problem#2:
an electromagnetic wave has a wavelength of 2 meters and a frequency of 1.5 x 10^8 hz. calculate its speed.
v = λf
problem#3:
a photon has a frequency of 2 x 10^14 hz. what is its energy?
problem#4:
a sound wave travels through the air at a speed of 343 meters per second. if the frequency of the wave is 256 hz (hertz), what is the wavelength of the sound wave?

Explanation:

Problem #1

Step1: Recall the speed of light

Radio waves are electromagnetic waves, so their speed \( v \) is the speed of light, \( v = 3\times10^{8}\, \text{m/s} \). The formula is \( v=\lambda f \), so we solve for \( f \): \( f=\frac{v}{\lambda} \).

Step2: Substitute values

Given \( \lambda = 3\, \text{m} \) and \( v = 3\times10^{8}\, \text{m/s} \), then \( f=\frac{3\times10^{8}}{3}=1\times10^{8}\, \text{Hz} \).

Step1: Use the formula \( v = \lambda f \)

We know \( \lambda = 2\, \text{m} \) and \( f = 1.5\times10^{8}\, \text{Hz} \).

Step2: Substitute values

\( v=2\times1.5\times10^{8}=3\times10^{8}\, \text{m/s} \).

Step1: Recall the photon energy formula

The formula for photon energy is \( E = hf \), where \( h = 6.626\times10^{-34}\, \text{J·s} \) (Planck's constant) and \( f = 2\times10^{14}\, \text{Hz} \).

Step2: Substitute values

\( E=6.626\times10^{-34}\times2\times10^{14}=1.3252\times10^{-19}\, \text{J} \) (approx \( 1.33\times10^{-19}\, \text{J} \) or in electron - volts, \( E=\frac{1.3252\times10^{-19}}{1.6\times10^{-19}}\approx0.828\, \text{eV} \), but usually in joules for this calculation).

Answer:

\( 1\times10^{8}\, \text{Hz} \)

Problem #2