Q

# Stuck here, help me understand: A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, th

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :

• Option 1)

680 Hz

• Option 2)

510 Hz

• Option 3)

340 Hz

• Option 4)

170 Hz

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As we learnt in

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

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

- wherein

$C=$ speed of sound

$V_{\Delta }=$ speed of source

$\nu _{0}=$ original frequency

$\nu {}'=$ apparent frequency

$\upsilon'_{air}=\left(\frac{340}{340-5} \right )\upsilon$

$\upsilon'_{ind}=\left(\frac{340}{340+5} \right )\upsilon$

$\therefore\ \; \upsilon'_{ind}-\upsilon_{air}=5$

$\therefore\ \; \upsilon'=\frac{340\times5}{10}$

$\upsilon'= 170\ Hz$

Correct option is 4.

Option 1)

680 Hz

This is an incorrect option.

Option 2)

510 Hz

This is an incorrect option.

Option 3)

340 Hz

This is an incorrect option.

Option 4)

170 Hz

This is the correct option.

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