Question

1. The speed of all electromagnetic waves in empty space is 3.00 × 108 m/s.
What is the wavelength of radio waves emit- ted at 96.9 MHz?
Answer in units of m.
2. What is the wavelength of visible light emit- ted at 4.6 × 108 MHz?
Answer in units of m.
3. What is the wavelength of X rays emitted at 3.4 × 1012 MHz?
Answer in units of m.

Answer 1

Answer:

1. 3.10 m

2. 0.65 m

3. $8.82\times 10^{-5}\ m$

Explanation:

Speed of light, s is given as the product of frequency and wavelength and expressed as s=wf where s is the speed of light, w is the wavelength in m and f is the frequency in Hz. Making wavelength, w the subject of the formula then $w=\frac {s}{f}$

and making substitution for all the three parts then

1.

Substituting f for 96.9 MHz which is equivalent to $96.9\times 10^{6}$ and s for $3.00\times 10^{8}$ then

$w=\frac {3.00\times 10^{8}}{96.9\times 10^{6}}=3.095975232\approx 3.10\ m$

2.

The frequency is given as $4.6\times 10^{8}$  note that the units should be Hz not MHz after giving it already raised to power 10 and substituting this for f and $3.00\times 10^{8$ for s then

$w=\frac {3.00\times 10^{8}}{4.6\times 10^{6}}=0.652173913\approx 0.65\ m$

3.

The frequency is given as $3.4\times 10^{12}$ and substituting this for f and $3.00\times 10^{8$ for s then

$w=\frac {3.00\times 10^{8}}{3.4\times 10^{12}}=8.82353\times 10^{-5}\approx 8.82\times 10^{-5}\ m$

Answer 2

The wavelengths for the given electromagnetic waves are:

(1) for radio wave: 3.1 m

(2) for visible light: 625 nm

(3) for X-rays: 88 pm

Calculating the wavelengths:

The speed of all electromagnetic waves in empty space is,

c = 3×10⁸ m/s

Now, the frequency (f) of an electromagnetic wave is associated with its wavelength (λ) given by the following expression:

f = c/λ

rearranging the term we get:

λ = c/f

(1) frequency of the radio wave is 96.9 MHz

f = 96.9×10⁶ Hz

so, the wavelength is given by:

λ = c/f = 3×10⁸/96.9×10⁶

λ = 3.1 m

(2) frequency of the radio wave is 4.6×10⁸ MHz

f = 4.8×10¹⁴ Hz

so, the wavelength is given by:

λ = c/f = 3×10⁸/4.8×10¹⁴

λ = 625 nm

(3) frequency of the radio wave is 3.4×10¹² MHz

f = 3.4×10¹⁸ Hz

so, the wavelength is given by:

λ = c/f = 3×10⁸/3.4×10¹⁸

λ = 88 pm

Learn more about wavelength:

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