Doppler Shift Formula and Doppler Shift Problems

Doppler Shift Formula :

wavelength shift ∆λ(mm3) in millimeter cube is divided by wavelength of the source not moving λ0 (mm3) 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(mm3) / λ0 (mm3)= v(m/s) / c (m/s)

Where,

∆λ → wavelength shift in (mm3)

λ0→ wavelength of the source not moving in (mm3)

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 vl is divided by speed of sound waves v(m/s) in meter per second is multiply by actual frequency of the sound wave fs(Hz) in Hertz. Hence the frequency formula has been written as,

F’ = (v(m/s) + vl) / (v(m/s) – vs(m/s)) fs(Hz)

Where,

Fs→ actual frequency of the sound wave in  (hz)

f ‘ → observed frequency

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

vl→ velocity of observer in (m/s)

vs → 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

vs = 60 m/s

fs = 110 Hz

vL = 0

Therefore, by the formula of Doppler shift:

F’ = (v + vl) / (v – vs) fs

       = 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

vs = 80 m/s

fs = 150 Hz

vL = 0

Therefore, by the formula of Doppler shift

F’ = (v + vl) / (v – vs) fs

= 150 × 343 + 0 / 343 -80

= 513.70Hz.

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