## Doppler Shift Formula :

wavelength shift ∆λ_{(mm}^{3}_{)} in millimeter cube is divided by wavelength of the source not moving λ_{0} _{(mm}^{3}_{)} in millimeter cube is the equal to the product of velocity of the source v_{(m/s)} in meter per second is divided by Speed of light c _{(m/s)} in meter per second. Hence the equation for Doppler Shift formula has been written as,

**∆λ _{(mm}^{3}_{)} / λ_{0} _{(mm}^{3}_{)}= v_{(m/s)} / c _{(m/s)}**

Where,

∆λ → wavelength shift in (mm^{3})

λ_{0}→ wavelength of the source not moving in (mm^{3})

v →velocity of the source in (m/s)

c →Speed of light in (m/s)

##### Frequency formula is given by,

Observed frequency F’ is equal to the product of speed of sound waves v_{(m/s)} in meter per second is the addition of velocity of observer v_{l} is divided by speed of sound waves v_{(m/s)} in meter per second is multiply by actual frequency of the sound wave f_{s(Hz) }in Hertz. Hence the frequency formula has been written as,

**F’ = (v _{(m/s)} + v_{l}) / (v_{(m/s)} – v_{s(m/s)}) f_{s(Hz)}**

Where,

F_{s→ }actual frequency of the sound wave in (hz)

f ‘ → observed frequency

v = speed of sound waves in (m/s)

v_{l}→ velocity of observer in (m/s)

v_{s} → velocity of the source in (m/s)

## Sample Problems :

### Example 1:

Calculate the frequency of the sound heard by a person in front of the object? In a object at 60 m/s is producing frequency at 110 Hz.

### Solution :

Given that,

v = 343 m/s

v_{s} = 60 m/s

f_{s} = 110 Hz

v_{L} = 0

Therefore, by the formula of Doppler shift:

F’ = (v + v_{l}) / (v – v_{s}) f_{s}

_{ }= 110 × 343 + 0 / 343 – 60

= 376.70Hz.

### Example 2:

Calculate the frequency of the sound heard by a person in front of the object? In a object at 80 m/s is producing frequency at 150 Hz.

### Solution :

Given that,

v = 343 m/s

v_{s} = 80 m/s

f_{s} = 150 Hz

v_{L} = 0

Therefore, by the formula of Doppler shift*: *

F’ = (v + v_{l}) / (v – v_{s}) f_{s}

= 150 × 343 + 0 / 343 -80

= 513.70Hz.