SNC2D WAVELENGTH & FREQUENCY PROBLEMS
- Frequency and wavelength of a wave have an inverse relationship.
- which means when one value increases, the other decreases.
For any wave, the speed (v) is calculated by using the formula v = fλ, v is replaced with the symbol for light, so we use c = fλ
where c = 3.00 x 10m/s (speed of light in vacuum)
f – frequency of the wave in Hertz (Hz).
λ – wavelength of the wave in metres.
Answer the following questions using GRASP (Show your work!) and write the final answer in scientific notation!
1. A laser based on yttrium aluminum garnet (called a YAG laser) emits a wavelength of 1064 nm. Calculate the frequency of the laser. Assume the speed of light, c = 3.00 x 10m/s.
G: c = 3.00 x 10m/s
λ = 1064 nm ´ 10-9 m/nm = 1.064 ´ 103 ´ 10-9 m
= 1.064 ´ 10-6 m
R: f in Hz
A: c = fλ à f = c/λ
S: f = (3.00 x 10m/s) ÷ (1.064 ´ 10-6 m)
f = 2.82 ´ 1014 Hz
P: The frequency of the YAG laser is 2.82 ´ 1014 Hz.
2. Determine the frequency of laser light with a wavelength of 622 nm. Assume the speed of light,
c = 3.00 x 10m/s.
3. An X ray has a frequency of 2.0 x 10Hz. Assume the speed of light is c = 3.00 x 10m/s. Calculate the wavelength in nanometres and in metres.
4. Red light has a frequency of 4.0 ´ 1014 Hz and a speed of 3.0 ´ 108 m/s. What is its wavelength in metres? In nanometres?
5. An earthquake creates a seismic wave that travels at 3500 m/s with a wavelength of 1750 m. Find the frequency of the seismic wave.
6. Calculate the frequency of a radar wave whose wavelength is 2 cm. Assume the speed of EMR is c = 3.00 x 10m/s.
7. Calculate the wavelength (in metres and nanometres) of green light whose frequency is 5.7 ´ 1014 Hz.
ANSWERS: 1) 2.82 ´ 1014 Hz 2) 4.82 ´ 1014 Hz 3) 1.5 ´ 10-10 m 4) 7.5 ´ 10-7 m 5) 2 Hz 6) 1.5 ´ 1010 Hz 7) 526 nm
SNC2D WAVELENGTH & FREQUENCY PROBLEMS SOLUTIONS
- Frequency and wavelength of a wave have an inverse relationship.
- which means when one value increases, the other decreases.
For any wave, the speed (v) is calculated by using the formula v = fλ, v is replaced with the symbol for light, so we use c = fλ
where c = 3.00 x 10m/s (speed of light in vacuum)
f – frequency of the wave in Hertz (Hz).
λ – wavelength of the wave in metres.
Answer the following questions using GRASP (Show your work!) and write the final answer in scientific notation!
1. A laser based on yttrium aluminum garnet (called a YAG laser) emits a wavelength of 1064 nm. Calculate the frequency of the laser. Assume the speed of light, c = 3.00 x 10m/s.
G: c = 3.00 x 10m/s
λ = 1064 nm ´ 10-9 m/nm = 1.064 ´ 103 ´ 10-9 m
= 1.064 ´ 10-6 m
R: f in Hz
A: c = fλ à f = c/λ
S: f = (3.00 x 10m/s) ÷ ( 1.064 ´ 10-6 m)
f = 2.82 ´ 1014 Hz
P: The frequency of the YAG laser is 2.82 ´ 1014 Hz.
2. Determine the frequency of laser light with a wavelength of 622 nm. Assume the speed of light,
c = 3.00 x 10m/s.
G: c = 3.00 x 10m/s
λ = 622 nm ´ 10-9 m/nm = 6.22 ´ 102 ´ 10-9 m = 6.22 ´ 10-7 m
R: f in Hz
A: c = fλ à f = c/λ
S: f = (3.00 ´ 10m/s) ÷ (6.22 ´ 10-7 m)
f = 4.82 ´ 1014 Hz
P: The frequency of the laser is 4.82 ´ 1014 Hz.
3. An X ray has a frequency of 2.0 x 10Hz. Assume the speed of light is c = 3.00 x 10m/s. Calculate the wavelength in nanometres and in metres.
G: c = 3.00 x 10m/s
f = 2.0 ´ 1018 Hz
R: λ in m & nm
A: c = fλ à λ = c/ f
S: λ = (3.00 ´ 10m/s) ÷ (2.0 ´ 1018 Hz)
λ = 1.5 ´ 10 -10 m ´ 109 nm/m
λ = 1.5 ´ 10 -1 nm
P: The wavelength is 1.5 ´ 10 -1 nm.
4. Red light has a frequency of 4.0 ´ 1014 Hz and a speed of 3.0 ´ 108 m/s. What is its wavelength in metres? In nanometres?
G: c = 3.00 x 10m/s
f = 4.0 ´ 1014 Hz
R: λ in m & nm
A: c = fλ à λ = c/ f
S: λ = (3.00 ´ 10m/s) ÷ (4.0 ´ 1014 Hz)
λ = 0.75 ´ 10 -6 m
λ = 7.5 ´ 10 -1 ´ 10 -6 m
λ = 7.5 ´ 10 -7 m ´ 109 nm/m
λ = 7.5 ´ 10 2 nm
P: The wavelength is 7.5 ´ 10 2 nm.
5. An earthquake creates a seismic wave that travels at 3500 m/s with a wavelength of 1750 m. Find the frequency of the seismic wave.
G: c = 3500 m/s
λ = 1750 m
R: f in Hz
A: c = fλ à f = c/λ
S: f = (3500 m/s) ÷ (1750 m)
f = 2 Hz
P: The frequency of the seismic wave is 2 Hz.
6. Calculate the frequency of a radar wave whose wavelength is 2 cm. Assume the speed of EMR is c = 3.00 x 10m/s.
G: c = 3.00 x 10m/s
λ = 2 cm ´ 10-2 m/cm = 2 ´ 10-2 m
R: f in Hz
A: c = fλ à f = c/λ
S: f = (3.00 ´ 10m/s) ÷ (2 ´ 10-2m)
f = 1.5 ´ 1010 Hz
P: The frequency of the radar wave is 1.5 ´ 1010 Hz.
7. Calculate the wavelength (in metres and nanometres) of green light whose frequency is 5.7 ´ 1014 Hz.
G: c = 3.00 x 10m/s
f = 5.7 ´ 1014 Hz
R: λ in m & nm
A: c = fλ à λ = c/ f
S: λ = (3.00 ´ 10m/s) ÷ (5.7 ´ 1014Hz)
λ = 0.526 ´ 10 -6 m
λ = 5.26 ´ 10 -1 ´ 10 -6 m
λ = 5.26 ´ 10 -7 m ´ 109 nm/m = 5.26 ´ 102 nm
P: The wavelength is 526 nm.