Question

all electromagnetic waves travel through the same type of matter at the same speed. a waves speed (v) in a given medium is related to its wavelength (λ) and frequency (f). wavelength is often measured in meters (m). frequency is usually measured in hertz (hz), where 1 hertz is equivalent to 1 wave cycle per second (s⁻¹).

v = fλ

the speed of light in a vacuum, c, is 2.998 × 10⁸ meters per second. so this equation relates the speed, wavelength, and frequency of a wave traveling through a vacuum.

c = fλ

complete the table to determine the frequency of each electromagnetic wave when it travels in a vacuum.

write your answers in scientific notation rounded to two decimal places.

electromagnetic wave wavelength (m) frequency (hz)
radio wave 14.7
infrared wave 9.43 × 10⁻⁷
x - ray 2.60 × 10⁻¹⁰

submit

work it out

not feeling ready yet? these can help:

Explanation:

Step1: Rearrange the formula for frequency

Given \(c = f\lambda\), we can solve for \(f\) as \(f=\frac{c}{\lambda}\)

Step2: Calculate the frequency of the radio wave

For the radio wave, \(\lambda = 14.7\space m\) and \(c = 2.998\times 10^{8}\space m/s\)

$$
LATEXBLOCK0
$$

Step3: Calculate the frequency of the infrared wave

For the infrared wave, \(\lambda=9.43\times 10^{-7}\space m\)

$$
LATEXBLOCK1
$$

Step4: Calculate the frequency of the X - ray

For the X - ray, \(\lambda = 2.60\times 10^{-10}\space m\)

$$
LATEXBLOCK2
$$

Answer:

• Radio wave: \(2.04\times 10^{7}\space Hz\)
• Infrared wave: \(3.18\times 10^{14}\space Hz\)
• X - ray: \(1.15\times 10^{18}\space Hz\)