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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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INDEX of physics notes: Properties and uses of electromagnetic radiation


This page contains online questions only. Jot down your answers and check them against the worked out answers at the end of the page

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.

Worked out ANSWERS to the wave equation questions

 

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.

Worked out ANSWERS to the wave equation questions

 

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?

Worked out ANSWERS to the wave equation questions

 

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

Calculate the frequency of the radiation.

Worked out ANSWERS to the wave equation questions

 

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

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

Worked out ANSWERS to the wave equation questions

 

Q6 A radio station is broadcasting its programmes with a radio frequency of 104 MHz.

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

Worked out ANSWERS to the wave equation questions

 

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.

Worked out ANSWERS to the wave equation questions

 

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?

Worked out ANSWERS to the wave equation questions

 

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?

Worked out ANSWERS to the wave equation questions

 

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

INDEX of notes: Properties and uses of electromagnetic radiation


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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INDEX of notes: Properties and uses of electromagnetic radiation

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 s to detect an echo.

How far away is the reflecting object? (you should know that 1 s = 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.

 

Q6 A radio station is broadcasting its programmes with a radio frequency of 104 MHz.

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)

 

INDEX of notes: Properties and uses of electromagnetic radiation

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