**PART 3**

**Beats:-**

-Interference of two harmonic waves of different frequencies and wavelength produces beats.

-In beats phenomenon interfering harmonic waves have slightely differing frequencies ν

_{1}and ν

_{2}such that

|ν

_{1}-ν

_{2}|<<(ν

_{1}+ν

_{2})/2

-Thus beats arises when two waves having slightly differing frequencies ν

_{1}and ν

_{2}and comparable amplitude are superposed. The beat frequency is

ν

_{beat}= ν

_{1}∼ ν

_{2}

-Musicians use beat phenomenon for tuning their instruments.

-For tuning an instrument for certain standard frequency it is sounded against a standard frequency and it is tuned untill the beats get disappeared.

**Doppler effect:-**

-Doppler effect is a change in the observed frequency of the wave when the source s and the observer o moves relative to the medium.

-There are three different ways where we can analyse this change in frequency.

(1) When observer is stationary and source is moving then change in frequency for source aproaching observer is

ν=ν

_{0}(1+v

_{s}/v)

where, v

_{s}=velocity of source relative to the medium

v=velocity of wave relative to the medium

ν=observed frequency of sound waves in term of source frequency

ν

_{0}=source frequency

-Change in frequencywhen source receeds from stationary observer is

ν=ν

_{0}(1-v

_{s}/v)

-Observer at rest measures higher frequency when source aproaches it and it measures lower frequency when source receeds from the observer.

(2)Doppler effect in frequency when observer is moving with a velocity v

_{o}towards source and the source is at rest is

ν=ν

_{0}(1+v

_{o}/v)

(3) If both source and observer are moving then frequency observed by observer is

ν=ν

_{0}(v+v

_{o})/(v+v

_{s})

and all the symbols have respective meanings as told earlier.

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