Classical Mechanics
# Waves

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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