# A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the sourcedetect sound to be of frequancies 480 Hz and 530 Hz. Their respective speedsare in m/s,(Given speed of sound = 300 m/s) Option 1) 12,16 Option 2) 12,18 Option 3) 16,14 Option 4) 8,18

Frequency of sound when source is stationary and observer is moving towards source. -

$\nu {}'= \nu _{0}.\frac{C+V_0}{C }$

- wherein

$C=$ speed of sound

$V_{0}=$ Speed of observer

$\nu _{0}=$ original frequency

$\nu {}'=$ apparent frequency

Frequency of sound when source is stationary and observer is moving away from source. -

$\nu {}'= \nu _{0}.\frac{C-V_0}{C }$

- wherein

$C=$ speed of sound

$V_{0}=$ Speed of observer

$\nu _{0}=$ original frequency

$\nu {}'=$ apparent frequency

$f_A=\frac{(300-V_A)}{300}\times 500=480$........................(1)

$f_B=\frac{(300+V_B)}{300}\times 500=530$........................(2)

From (1)

$300-V_A=288$

$V_A=12 \: \: m/s$

From (2)

$300+V_B=318$

$V_B=18 \: \: m/s$

Option 1)

12,16

Option 2)

12,18

Option 3)

16,14

Option 4)

8,18

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