The Doppler Effect Practice Problems

An asteroid crashes into the earth's atmosphere creating a cone-shaped shock wave. The angle between the shock wave and the asteroid's direction of motion is 44.0°. Take the speed of sound at high altitudes to be 295 m/s. Determine the asteroid's Mach number for that instant.

A police car is chasing a large vehicle at a speed of 33.0 m/s. The siren on the police car is emitting sound at a frequency of 1400 Hz. The vehicle is running away at a speed of 22.0 m/s. Determine the frequency of the sound reflected by the large vehicle as heard by police in the police car. 

An ambulance behind a wide-load truck driving in the same direction emits an alert tone at 1500 Hz. The ambulance moves at 28.0 m/s and the truck moves at 14.0 m/s. Determine the wavelength of the waves reflected by the truck's load measured relative to the ambulance. 

A truck driving at 16.5 m/s emits a sound of frequency 420 Hz from its horn in motionless air. Calculate the frequency heard by a driver in a vehicle traveling in the opposite direction and receding from the truck at 25.0 m/s.

A car driving at 15 m/s hoots at a frequency of 410 Hz in the motionless air. Determine the frequency heard by a driver in another car moving at 25 m/s in the opposite direction and approaching the hooting car. 

A 2.0 W, 2.5 KHz sound emitter is released 180 m above a detector. The atmospheric temperature is 22°C. Find the i) frequency and ii) the sound intensity level detected by the detector 5.5 s from the instant the emitter was released.

A motorcycle rider blows a whistle as he rides towards a stationary observer at 65 km/h. The whistle emits a 2.5 kHz frequency wave, and the speed of sound in the air at that instant is 342 m/s. Determine the frequency heard by the observer.

A whistle (supplied by a stream of air) emitting sound at 3.0 kHz is fixed to a 1.6 m from the axis of a rotating blade. The blade spins in a horizontal circle at 360 rpm. If the sound undergoes the Doppler effect, work out the greatest and least frequencies detected by an observer.

A self-driving drone navigates in space by emitting bursts of sound waves and detecting reflections from objects.  If a navigation sound has a frequency of 22 kHz, determine the speed and direction of the drone relative to an object if it detects a frequency of 18 kHz.

A siren on a blazing house emits sound at a frequency f. A firefighter approaches the siren on the blazing house at a speed v_f. Derive an expression of the frequency, f_r, of waves reflecting from the fire truck towards the siren. Express the result using f, v_f, and speed of sound in air, v.

A teacher develops a simple method to investigate the fundamentals of the Doppler effect using acoustic waves. The teacher uses a tuning fork to produce a sound of frequency f_s. During the experiment, a student riding a bike equipped with a microphone and a sound system approaches the tuning fork at a constant speed. The sound system emits a sound signal toward the class students sitting behind the tuning fork. Assume that students hear a sound with a frequency of 1.03 f_s from the sound system. Calculate the bike's speed.

What is the received sound wave frequency value if a sonar device sends out sound waves at 60.0 kHz and receives them back from a car that is moving directly away from the device at a speed of 30.0 m/s? [Hint: $f^{\prime}=\frac{\left(v-v_0\right)}{\left(v+v_0\right)}f$ , where $v$ = 343 m/s is the velocity of sound and $v_0$ is the velocity of observer.]

What is the speed of a moving car when two cars, where one car is stationary, honk their horns at 506 Hz, and a person located in the stationary car hears a 5.5 Hz beat frequency as the other car approaches them? [Hint: $f^{\prime}=f\frac{v_{snd}}{\left(v_{snd}-v_{source}\right)}$ where $v_{snd}$ = 343 m/s represents the sound speed in air].

Two musicians are both playing the same note at 440 Hz. A listener is moving towards one musician and away from the other at 2.0 m/s. What beat frequency will the listener perceive?

A train moving at 115 km/h blows its whistle with a frequency of 1320 Hz. A physics student attempts to measure the apparent frequency of the train's whistle on a bicycle moving at 72.0 km/h in the opposite direction toward the train. What is the measured frequency of the train's whistle before and after she passes the train? Assume that the speed of sound in air is 343 m/s.

Engineers are installing a siren atop a tower. For testing they let it emit a sound of frequency 1200 Hz. The wind velocity is 10 m/s heading south. What will be the perceived frequency for observers located east of the siren?

A car alarm emits a sound with a frequency of 800 Hz. A breeze is blowing at a speed of about 6 m/sec eastwards. What will be the observed frequency moving westwards towards the alarm at a speed of about 4 m/sec? Assume that the temperature is around 20°C.

A train horn emits a sound at a frequency of 850 Hz. Pedestrians are located at rest, due east of the horn. At what frequency will the pedestrians hear if the wind blows from the east at a velocity of 16.0 m/s (heading west)?

A musician is playing a note of frequency 450 Hz on a stationary loudspeaker. The wind is blowing at a velocity of 14 m/s from the west to the east. Calculate what frequency the note would appear to be to an observer heading south toward the loudspeaker at a velocity of 20 m/s. Assume that the temperature T = 25°C.

An ambulance, with a siren frequency of 1250 Hz, is moving at $1.00\times 10^2$ km/ h and passes a car traveling at 90.0 km/h. Find the two frequencies heard in the car traveling in the same direction as the ambulance. Use: the speed of sound $=343\mathrm{~m}/\mathrm{s}$ .

The foghorn of a stationary ship emits a sound at a frequency of 300 Hz. The wind blows at 20.0 m/s from the west (heading east). Given that the temperature is T = 20°C, determine the frequency heard by stationary observers located east of the stationary ship.

A stationary train whistles a sound of frequency 850 Hz. To a stationary observer located north of the train, what should be the frequency that can be heard when the wind velocity is 10.0 m/s blowing from the east (heading west)? Assume $T=20^{\circ }\text{C}$.