An automobile is driving North at a speed of 30 m/s toward a cliff with a tunnel

Question

An automobile is driving North at a speed of 30 m/s toward a cliff with a tunnel opening facing South. The wind is blowing toward the North West at a speed of 40 m/s. The horn on the car emits a frequency of 500 Hz. and is echoing off of the cliff wall, Calculate the frequencies heard by the driver in the automobile, Calculate the frequencies heard by a bystander on the side of the road, if the car is approaching. The velocity of sound is 340 m/s. Draw a nice clear simple picture of this situation.

Explanation / Answer

the sound is emmited in the direction theta angle from the north so that the resultant between velocity of sound and velocity of wind is towards north...

resultant velocity of sound=367 m/s 12 degrees east of north.

so frequency heard by driver=500*(367+30)/(367-30)=589 Hz

frequency heard by bystander=500*367/(367-30)=544 Hz

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