Find the wavelength for an AM radio station with frequency 1000Hz. Speed of radio waves in vacuum is equal to the speed of light
Answers
Answer:
Explanation:
The equation that relates wavelength, frequency, and speed of light is
c
=
λ
⋅
ν
c
=
3.00
×
10
8
m/s
(the speed of light in a vacuum)
λ
= wavelength in meters
ν
= frequency in Hertz (Hz) or
1
s
or
s
−
1
.
So basically the wavelength times the frequency of an electromagnetic wave equals the speed of light.
FYI,
λ
is the Greek letter lambda , and
ν
is the Greek letter nu (it is not the same as a v).
To find wavelength (
λ
), the equation is manipulated so that
λ
=
c
ν
.
Answer:
Explanation:the equation that relates wavelength, frequency, and speed of light is
c
=
λ
⋅
ν
c
=
3.00
×
10
8
m/s
(the speed of light in a vacuum)
λ
= wavelength in meters
ν
= frequency in Hertz (Hz) or
1
s
or
s
−
1
.
So basically the wavelength times the frequency of an electromagnetic wave equals the speed of light.
FYI,
λ
is the Greek letter lambda , and
ν
is the Greek letter nu (it is not the same as a v).
To find wavelength (
λ
), the equation is manipulated so that
λ
=
c
ν
.
EXAMPLE PROBLEM 1
What is the wavelength of a electromagnetic wave that has a frequency of
4.95
×
10
14
Hz
?
Given or Known:
frequency or
ν
=
4.95
×
10
14
Hz
or
4.50
×
10
14
s
−
1
c
=
3.00
×
10
8
m/s
Unknown:
Wavelength or
λ
Equation:
c
=
λ
⋅
ν
Solution:
λ
=
c
ν
=
3.00
×
10
8
m
s
4.95
×
10
14
s
−
1
=
6.06
×
10
−
7
m
But what if you don't know the frequency? Can you still find the wavelength? Yes. An equation that relates energy and frequency is:
E
=
h
ν
E
= energy in Joules
(
J
)
h
= Planck's constant =
6.626
×
10
−
34
J
⋅
s
ν
= frequency =
Hz
or
s
−
1
To find frequency, the equation is manipulated so that
ν
=
E
h
Once you have frequency, you can use the first equation
c
=
λ
⋅
ν
to find the wavelength.
EXAMPLE PROBLEM 2
What is the wavelength of an electromagnetic wave having
3.28
×
10
−
19
J
of energy?
Given or Known:
E
=
3.28
×
10
−
19
J
h
=
6.626
×
10
−
34
J
⋅
s
Unknown:
frequency,
ν
Equation:
E
=
h
ν
Solution: Part 1
ν
=
E
h
=
3.28
×
10
−
19
J
6.626
×
10
−
34
J
⋅
s
=
4.95
×
10
14
Hz
or
4.95
×
10
14
s
−
1
Solution: Part 2
λ
=
c
ν
=
3.00
×
10
8
m
s
4.95
×
10
14
s
−
1
=
6.06
×
10
−
7
mhe equation that relates wavelength, frequency, and speed of light is
c
=
λ
⋅
ν
c
=
3.00
×
10
8
m/s
(the speed of light in a vacuum)
λ
= wavelength in meters
ν
= frequency in Hertz (Hz) or
1
s
or
s
−
1
.
So basically the wavelength times the frequency of an electromagnetic wave equals the speed of light.
FYI,
λ
is the Greek letter lambda , and
ν
is the Greek letter nu (it is not the same as a v).
To find wavelength (
λ
), the equation is manipulated so that
λ
=
c
ν
.
EXAMPLE PROBLEM 1
What is the wavelength of a electromagnetic wave that has a frequency of
4.95
×
10
14
Hz
?
Given or Known:
frequency or
ν
=
4.95
×
10
14
Hz
or
4.50
×
10
14
s
−
1
c
=
3.00
×
10
8
m/s
Unknown:
Wavelength or
λ
Equation:
c
=
λ
⋅
ν
Solution:
λ
=
c
ν
=
3.00
×
10
8
m
s
4.95
×
10
14
s
−
1
=
6.06
×
10
−
7
m
But what if you don't know the frequency? Can you still find the wavelength? Yes. An equation that relates energy and frequency is:
E
=
h
ν
E
= energy in Joules
(
J
)
h
= Planck's constant =
6.626
×
10
−
34
J
⋅
s
ν
= frequency =
Hz
or
s
−
1
To find frequency, the equation is manipulated so that
ν
=
E
h
Once you have frequency, you can use the first equation
c
=
λ
⋅
ν
to find the wavelength.
EXAMPLE PROBLEM 2
What is the wavelength of an electromagnetic wave having
3.28
×
10
−
19
J
of energy?
Given or Known:
E
=
3.28
×
10
−
19
J
h
=
6.626
×
10
−
34
J
⋅
s
Unknown:
frequency,
ν
Equation:
E
=
h
ν
Solution: Part 1
ν
=
E
h
=
3.28
×
10
−
19
J
6.626
×
10
−
34
J
⋅
s
=
4.95
×
10
14
Hz
or
4.95
×
10
14
s
−
1
Solution: Part 2
λ
=
c
ν
=
3.00
×
10
8
m
s
4.95
×
10
14
s
−
1
=
6.06
×
10
−
7
m