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Structure Of Atom

Question
CBSEENCH11005235

What are the characteristics of waves?

Solution

The following parameters are used to characterise these waves:
(i) Wavelength: It is defined as the distance between two adjacent crests or troughs of the wave. It is denoted by lambda (λ). It is generally expressed in metres; Angstroms (Å) or nanometres (nm).
1 Å = 10-10m
1 nm = 10-9 m

(ii) Frequency: It is defined as number of waves which pass through a given point in one second. It is denoted by v (nu) and is measured in cycles per second (cps) or simply reciprocal seconds (sec-1). It is also expressed in terms of Hertz (Hz).

It is inversely proportional to the wavelength.
straight v space straight alpha space 1 over straight lambda
(iii) Velocity: The distance travelled by the wave in one second is called the velocity of the wave. It is denoted by c and is equal to the product of wavelength and frequency.
c =vλ
straight i. straight e. space space space straight v space equals space straight c over straight lambda
The units of velocity are ms-1 or cm s-1.
Light and all other types of electromagnetic radiations travel through space with the same velocity i.e. 3 x 10-8 ms-1.
(iv) Amplitude: The height of the crest or the depth of the trough or distance of maximum displacement is called amplitude. It is denoted by a. It determines the density or brightness of a beam of light.
(v) Wave number: It is defined as the number of wavelengths per unit of length and is equal to the inverse of wavelength expressed in centimetres. It is denoted by ⊽ cm-1 or in-1.
                              straight v with bar on top space equals space 1 over straight lambda                      ...(1)
But                          straight c space equals vλ
or                  1 over straight lambda space equals straight v over straight c                              ...(2)
therefore  From (1) and (2),
                            straight v with bar on top space equals space straight v over straight c
or            straight c space cross times space straight v with bar on top space equals space straight v