Doppler Effect

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{4}A_{44} Base Sequence = 12735 String Sequence = 12735 - 4 - 44 **

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(a) What is the relationship between the frequency of the sound from the siren of the futuristic ambulance illustrated above and the frequency heard by an observer if both ambulance and observer are approaching each other at velocities v_{a} and v_{o} respectively?

(b) If ambulance and observer are moving in opposite directions at velocities v_{a} and v_{o} respectively?

**The strings**:
S_{7}P_{4}A_{44} (Motion - Oscillatory Motion).
**The math**:

Pj Problem of Interest is of type *motion* (oscilatory).

When the source of sound and the receiver (hearer) of sound are in relative motion, the frequency of the sound heard by the receiver is different from the frequency of the sound emitted by the source. This change in freqency is referred to as the *Doppler effect*.

(a) The relationship between the frequencies when source of sound and receiver of sound are approaching each other is as follows:
** f _{r} = [(c + v_{r})/(c - v_{s})]f_{s}**

Where f

f

c is velocity of sound (331.45 m/sec)

v

v

So, for the ambulance and observer approaching each other we have:

f

Sound waves pile up, therefore shorter wavelengths and higher frequency sound reaches the receiver.

(b) The relationship between the frequencies when source of sound and receiver of sound are moving awat from each other:

The signs of the respective velocities are negative.

So, for the ambulance and observer moving away from each other we have:

f

Sound waves spread out, therefore longer wavelengths and lower frequency sound reaches the receiver.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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