Question 81: Waves

Question

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]

Accepted Answer

Given, v
A
= v
B
= 7.2 kmh
$$-$$1
$$ = {{72} \over {10}} 	imes {5 \over {18}}$$ = 2 ms
$$-$$1
Frequency of source, f
s
= 676 Hz
Speed of sound in air, v = 340 ms
$$-$$1
Let f
0
be the frequency heard by each driver.
By using Doppler effect for A,
$$(v - {v_A}){f_s} = (v + {v_B}){f_0}$$
$$ \Rightarrow {f_0} = \left( {{{v + {v_A}} \over {v - {v_B}}}} ight){f_s} = \left( {{{340 + 2} \over {340 - 2}}} ight)676 = {{342} \over {338}} 	imes 676 = 684$$ Hz
Now, beat frequency $$ = {f_0} - {f_s} = 684 - 676 = 8$$ Hz

Waves

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]

Integer / Numeric Answer Type