SITEMAP   School Physics Notes: Electromagnetic spectrum 2. EMR wave calculations

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Electromagnetic spectrum: 2. Examples of worked out wave equation calculations involving electromagnetic radiation - formula relating speed (m/s), wavelength (m) and frequency (Hz, s-1)

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2. Examples of wave equation calculations involving electromagnetic radiation

You should know that all waves obey the same wave equation:

v = λ x f  where

v is speed in metres per second, m/s,

for electromagnetic radiation calculations, the speed in vacuum/air is taken as 3.0 x 108 m/s

λ  is wavelength in metres, m

f is frequency in hertz, Hz (per sec)

wave equation rearrangements:  f = v / λ   and   λ = v / f f = v / λ  and  λ = v / f

Note that you are not required to recall the value of the speed of electromagnetic waves through a vacuum ...

.. it is very big, 'speed of light', v, is taken to be exactly 3.0 x 108 m/s AND to be used in all questions

Be able to do examples of calculations using the wave speed formula and its rearrangements.

speed (m/s)  = wavelength (m) x frequency (Hz, s-1)

v = f x λ  *  f = v / λ  *  λ = v / f

You may also need:

speed (m/s) = distance (m) / time (s)

period (s) = 1 / f (Hz)

PLEASE , it is much better to be able to rearrange the wave equation than use a triangle.

Q1 A red light beam has a wavelength of 650 nm.

Calculate the frequency of red light photons.

Q2 A green laser light beam has a fixed frequency of 5.90 x 1014 Hz

Calculate the wavelength of the laser light in m and nm.

Q3 The time period of a electromagnetic radio wave is 5.0 x 10-5 seconds

(a) What is the frequency of the radio wave?

(b) If the 'speed of light' is 3.0 x 108 m/s, calculate the wavelength of the radio wave in m.

(c) If the distance from the transmitting radio station to your radio is 200 km, how long does it take the signal to reach you?

Q4 A wave of electromagnetic radiation has a wavelength of 25 cm

Calculate the frequency of the radiation.

Q5 A scanning device sends out a pulse of microwave radiation that takes15 µs to detect an echo.

How far away is the reflecting object? (you should know that 1 µs = 10-6 s)

Calculate the wavelength of the radio signal. (you should know 1 MHz = 106 Hz)

Q7 For radio astronomy, the shortest wavelength of radio waves that can pass through the Earth's atmosphere is 100 m.

Calculate the maximum frequency of radio waves that can be detected.

Q8 A satellite is 75 km above the Earth's surface. (speed of light 3.00 x 108 m/s)

What is the shortest time that a microwave signal would take to reach the satellite from the Earth's surface?

Q9 A red light wave has a wavelength of 7.0 x 10-7 m. (speed of light 3.00 x 108 m/s)

What is the frequency of the red light wave?

Need Q using kHz, X-rays, gamma etc. maybe a red-shift Q ?

Keywords, phrases and learning objectives for electromagnetic radiation spectrum

Be able to use and rearrange the wave equation for electromagnetic radiation to perform calculations and solve problems.

Know the formula relating speed m/s, wavelength m and frequency Hz s-1

i.e. v = f x λ  *  f = v / λ  *  λ = v / f

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Worked out ANSWERS to the wave equation questions

Q1 A red light beam has a wavelength of 650 nm.

Calculate the frequency of red light photons.

v = f x λ  *  f = v / λ = 3 x 108 / (658 x 10-9) = 4.62 x 1014 Hz

Q2 A green laser light beam has a fixed frequency of 5.90 x 1014 Hz

Calculate the wavelength of the laser light in m and nm.

v = f x λ  *  λ = v / f = 3 x 108 / (5.90 x 1014) = 5.08 x 10-7 m

1 nm = 10-9 m, so wavelength = 5.08 x 10-7 x 109 = 508 nm

Q3 The time period of a electromagnetic radio wave is 5.0 x 10-5 seconds

(a) What is the frequency of the radio wave?

period = 1 / frequency

f = 1 / period = 1 / (5.0 x 10-5) = 2.0 x 104 Hz

(b) If the 'speed of light' is 3.0 x 108 m/s, calculate the wavelength of the radio wave in m.

λ = v ÷ f = 3.0 x 108 / 2.0 x 104 = 1.5 x 104 m

(c) If the distance from the transmitting radio station to your radio is 200 km, how long does it take the signal to reach you?

The speed formula is v = d / t,  so  t = d / v = (200 x 1000) / (3.0 x 108) = 6.7 x 10-4 s

Q4 A wave of electromagnetic radiation has a wavelength of 25 cm

Calculate the frequency of the radiation.

25 cm = 25 / 100 = 0.25 m

v = f x λ  *  f = v / λ  = 3 x 108 / 0.25 = 1.2 x 109 Hz

Q5 A scanning device sends out a pulse of microwave radiation that takes15 µs to detect an echo.

How far away is the reflecting object? (you should know that 1 µs = 10-6 s)

v = d / t, so d = v x t = (3 x 108) x (15 x 10-6) = 4500 m

BUT, this the total distance 'there and back', so the reflecting object is 4500 / 2 = 2250 m away.

Calculate the wavelength of the radio signal. (you should know 1 MHz = 106 Hz)

v = f x λ, so  λ = v / f = (3 x 108) / (104 x 106) = 2.89 m (3 sf)

Q7 For radio astronomy, the shortest wavelength of radio waves that can pass through the Earth's atmosphere is 100 m.

Calculate the maximum frequency of radio waves that can be detected.

v = f x λ  *  f = v / λ  = 3 x 108 / 100 = 3 x 106 Hz

Q8 A satellite is 75 km above the Earth's surface. (speed of light 3.00 x 108 m/s)

What is the shortest time that a microwave signal would take to reach the satellite from the Earth's surface?

s = d / t,  t = d / s = (75 x 1000) / (3.00 x 108) = 2.50 x 10-4 seconds

Q9 A red light wave has a wavelength of 7.0 x 10-7 m. (speed of light 3.00 x 108 m/s)

What is the frequency of the red light wave?

v = f x λ  *  f = v / λ  = 3 x 108 / (7.0 x 10-7 m) = 4.29 x 1014 Hz  (3 sf)

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