Doppler effect of Sound

DOPPLER EFFECT OF SOUND

INTRODUCTION

The Doppler Effect or Doppler Shift named after Austrian physicist Christian Doppler is a phenomenon of change in frequency or wavelength of a wave for an observer moving relative to the source. When the source [body emitting sound] is in motion toward the observer, waves [ex: sound, light] are compressed leading to shorter wavelengths or greater frequency. Similarly when the source moves away from the observer, the waves are spread apart leading to longer wavelengths or smaller frequency. We’ll discuss the effect of Doppler shift in everyday life particularly two cases where Doppler shift doesn’t occur.

ASSUMPTIONS

      1. The atmospheric air has standard temperature and pressure conditions

·         Temperature T = 298 K or 25°C or 77°F

·         Pressure = 1 bar = 10⁵ N/m²

2    2. The effect of humidity on sound is negligible

3    3. The amplitude of sound is negligible

4    4. The air molecules do not move with respect to source and observer

CALCULATION

The Doppler shift arises when two observers in different frames register two different values of frequency while there is only one original frequency which is the source frequency.

The equation for Doppler shift is given by,

f’ = f₀*{[V ± V_o]/[V ± V_s]} (Eq. 1)

f₀ – Original frequency (Hz)

f’ – Apparent or observed frequency (Hz)

V – Velocity of Sound in air at standard temperature and pressure conditions (m/s) {V = 343 m/s}

V_o – Velocity of observer (m/s)

V_s – Velocity of Source (m/s)

There are two cases where the apparent and original frequency will be the same.

CASE # 1

If both source and observer are stationary, no matter how far or near they are, both will register the same frequency. When both source and observer are stationary,

V_o = V_s = 0 (Eq. 2)

Substitute equation (2) in equation (1),

f’ = f₀*{[V ± 0]/[V ± 0]}

f’ = f₀

CASE # 2

If both source and observer are moving in same direction with the same velocity, they both will register the same frequency. In this case,

V_o = V_{s  (Eq. 3)}

Substitute equation (3) in equation (1),

f’ = f₀*{[V ± V_s]/[V ± V_s]}

f’ = f₀

CONCLUSION

Thus the Doppler shift was explained and the two cases where the shift doesn’t occur were also explained.