Name: The Speed of a Travelling Wave
Uploaded: 2019-07-19
Duration: 4 min 21 s
Description: How do you derive the wave speed of the travelling wave, and what is the relation of the wave speed with wave frequency, wavelength and time period? Let's le...

Question

Speed of light in vacuum is

3 \times 10^{8} m s^{- 1}

. Range of wavelength of visible light is

4000 \overset{o}{A} - 7000 \overset{o}{A}

. Find the range of frequency of visible light.

Accepted Answer

Given that the speed of light in vacuum is, $v = 3 \times 10^{8} m s^{- 1}$ .
Range of wavelength, $λ$ of visible light is, $4000 \overset{o}{A} to 7000 \overset{o}{A}$ . We need to calculate frequency, $f$ .
Let, $λ_{m i n} = 4000 \overset{o}{A} = 4 \times 10^{- 7} m and λ_{m a x} = 7000 \overset{o}{A} = 7 \times 10^{- 7} m$ .
Speed of the light wave is, $v = f λ \Rightarrow f = \frac{v}{λ} \Rightarrow f \propto \frac{1}{λ}$ .

The range of frequency of visible light is,
$f_{m a x} = \frac{v}{λ_{m i n}} = \frac{3 \times 10^{8}}{4 \times 10^{- 7}} = 0.75 \times 10^{15} = 7.5 \times 10^{14} Hz$ .
$f_{m i n} = \frac{v}{λ_{m a x}} = \frac{3 \times 10^{8}}{7 \times 10^{- 7}} = 0.43 \times 10^{15} = 4.3 \times 10^{14} Hz .$
Hence, the range of the frequency of the wave is, $4.3 \times 10^{14} Hz to 7.5 \times 10^{14} Hz$ .

D. C. Pandey Solutions for Chapter: Wave Motion, Exercise 4: INTRODUCTORY EXERCISE 17.4

D. C. Pandey Physics Solutions for Exercise - D. C. Pandey Solutions for Chapter: Wave Motion, Exercise 4: INTRODUCTORY EXERCISE 17.4

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