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Wave Calculations Tutorial

The document discusses the relationships between various properties of waves including velocity, wavelength, frequency, and wave number. It provides formulas for calculating these values, such as velocity = frequency x wavelength. It then works through 5 examples of calculations involving radio waves and electromagnetic radiation, such as calculating wavelength given frequency. These examples demonstrate how to use the formulas to find values when any two properties are given.

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120 views7 pages

Wave Calculations Tutorial

The document discusses the relationships between various properties of waves including velocity, wavelength, frequency, and wave number. It provides formulas for calculating these values, such as velocity = frequency x wavelength. It then works through 5 examples of calculations involving radio waves and electromagnetic radiation, such as calculating wavelength given frequency. These examples demonstrate how to use the formulas to find values when any two properties are given.

Uploaded by

DYES Motion Graphics
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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TUTORIAL 25

UNIT 2

STRUCTURE OF ATOM
NUMERICAL FROM THE RELATION C=ν x λ

By S.J.C.
Formulae to be remember:
• Relation between velocity of a wave (c), wavelength(λ) and frequency (ν):
c =ν x λ
or, λ= c /ν
or, ν= c /λ
Where, c is velocity of light , c= 3 x 108 m/s
• Relation between wave number (ῡ) and wavelength (λ) :
ῡ=1/λ

• Units of wavelength (λ): • Units of frequency (ν): • Units of wave number


cm, m, nm, pm and Å Hz (Hertz) or simply sec-1 or s-1 (ῡ):

1 Å (Armstrong)= 10-8cm= 10-10m it is just reciprocal of


1 Hz= 1 cycle/ sec
unit of wavelength such
1 nm (nanometre)= 10-9m 1 kHz= 103Hz = 103 s-1 as m-1, cm-1 etc.
1 pm (picometre)= 10-12m 1Mhz= 106Hz = 106 s-1
1. Calculate the wave number and frequency of yellow radiation having wavelength
5800Å.
Solution: Given, wavelength (λ)= 5800Å= 5800 x 10-10 m
Therefore, wave number, ῡ=1/λ
=1/5800 x 10-10 m
=1.72 x 106 m-1
Again, frequency ν =c / λ
here, c = velocity of light= 3 x 108 m/s

3 x 108 m/s
therefore, frequency, ν =
5800 x 10-10m
= 5.172 x 1014 s-1
2. Calculate the frequency of infrared radiation having wavelength 3 x 106 nm.
Solution: Given, wavelength (λ)= 3 x 106 nm = 3 x 106 x 10-9 m= 3 x 10-3 m
Therefore, frequency ν =c / λ
here, c = velocity of light= 3 x 108 m/s

3 x 108 m/s
therefore, frequency, ν = 3 x 10-3 m
= 1011 s-1
3. Calculate the wave number of a radiation having frequency 4 x 1014Hz.
Solution: Given, frequency ν =4 x 1014Hz.= 4 x 1014s-1
Since, from the relation c= ν x λ (where c= 3 x 108 m/s)
Now, λ= c/ ν
3 x 108 m/s
λ= 4 x 1014s-1 = 0.75 x 10-6m
again, ῡ=1/λ
= 1/ 0.75 x 10-6m = 1.33 x 10 6 m-1
4. A particular radio station broadcast at frequency of 1120 kHz and another radio
station broadcast at a frequency at 98.7 MHz . What are the wavelength of these
radio station.
Solution: For the first radio station,
Given frequency ν= 1120kHz =1120 x 103Hz= 1120 x 103 s-1
Since, c =ν x λ
or, λ= c /ν ( where, c is velocity of light, c= 3 x 108 m/s)
8
Therefore, wavelength of the first radio station, λ = 3 x 10 m/s
3 -1
=257.85 m
1120 x 10 s

For the second radio station,


Given frequency ν= 98.7 MHz =98.7 x 106Hz= 98.7 x 106 s-1
Since, c =ν x λ
or, λ= c /ν ( where, c is velocity of light, c= 3 x 108 m/s)
3 x 108 m/s
Therefore, wavelength of the second radio station, λ = =3.0395 m
98.7 x 106 s-1
5. How long would it take a radio wave of frequency 6 x 103 Hz to travel from Mars to
Earth, a distance of 8 X 107 km?

Solution: All radiations can travel in vacuum in a velocity of light 3 x 108 m/s.
Given distance from Mars to Earth is= 8 X 107 km= 8 X 107 x 103 m= 8 X 1010 m.
Since velocity= distance/ time
therefore, time= distance/ velocity
8 X 1010 m
Hence, the time required =
3 x 108 m/s
=2.66 x 102 s
= 4 min 26 s
Home work:
1. The Vividh Bharati station of All India Radio, Delhi broadcast in a
frequency of 1368 kHz. Calculate the wavelength of the radio wave
emitted by their transmitter.
2. “The visible region of a spectrum have the wavelength range from
Violet (400 nm) to red (750 nm)”- convert these wavelength to
frequencies.
3. Calculate the wave number of a radiation of frequency
5.172 x 1014Hz.

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