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Waves

Waves are disturbances that transport energy without transporting mass. Learn the mechanism underlying sound, deep ocean swells, light, and even the levitation of objects in mid air.

Doppler Effect

         

As shown in the above diagram, person \( A \) driving a car with speed \( v_A = 17 \text{ m/s} \) hears a siren sound with frequency \( f_ A = 737 \text{ Hz}\) at a distance of \( d = 141 \text{ m}\) behind him, coming from an ambulance chasing his car with speed \( v_{am} = 34 \text{ m/s}.\) What is the approximate frequency of the siren sound heard in the ambulance?

Assumption

  • The speed of sound is \( u = 340 \text{ m/s}. \)

An ambulance sounding a siren of frequency \( f_{am} = 687 \text{ Hz} \) is traveling towards a vertical reflecting wall with a speed of \( v_{am} = 15 \text{ m/s}. \) If the wall is moving in same direction as the ambulance with a speed of \( v_w = 5 \text{ m/s},\) what is the approximate beat frequency heard by the driver of the ambulance?

Assumption

  • The speed of sound is \( u = 340 \text{ m/s}. \)

A person is riding a merry-go-round which has a radius of \( r = 3 \text{ m} \) and an angular speed of \( \omega = 3 \text{ rad/s}. \) If the person starts to blow a whistle of frequency \( f= 485 \text{ Hz},\) what is the approximate highest frequency heard by a listener at rest a long distance away?

Assumption

  • The speed of sound is \( u = 340 \text{ m/s}. \)

As shown in the above diagram, person \( A \) drives a car with speed \( v = 16 \text{ m/s} \) at a distance of \( d = 119 \text{ m} \) away from an ambulance standing still and sounding a siren with frequency \( f_ A = 763 \text{ Hz}. \) What is the approximate frequency of the siren sound heard in the car?

Assumption

  • The speed of sound is \( u = 340 \text{ m/s}. \)

As shown in the above diagram, person \( A \) hears an ambulance which heads towards him at a speed of \( v = 14 \text{ m/s} \) sounding a siren with frequency \( f_A = 775 \text{ Hz}\) at a distance of \( d = 104 \text{ m} \) away from him. What is the approximate frequency of the siren sound heard in the ambulance?

Assumption

  • The speed of sound is \( u = 340 \text{ m/s}. \)
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