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In this lesson, we will learn how to calculate the change in the frequency of waves that are emitted by a source that is moving relative to the observer.

Q1:

A hawk swoops down to catch a mouse, screeching as it does so. The hawk approaches the mouse at a speed of 25.0 m/s, and the frequency of the screech is 3 5 0 0 Hz. What is the frequency of the screech as heard by the mouse? Use a value of 331 m/s for the speed of sound in air.

Q2:

A commuter train approaches a crossing and blows its horn to make a note of frequency 200 Hz. An observer at the crossing measures the frequency of the train’s horn as 208 Hz. The speed of sound in the train’s vicinity is 335 m/s.

What is the speed of the train?

If the train’s speed remains constant, what frequency does the observer measure as the train recedes from them?

Q3:

An ambulance with a siren blaring is approaching an accident scene. The ambulance is moving at 70.00 mph. A nurse is approaching the scene from the opposite direction, running at . What frequency does the nurse observe? Assume the speed of sound is .

Q4:

What is the minimum speed at which a source must travel toward you for you to be able to hear that its frequency is Doppler shifted? That is, what speed produces a shift of 0 . 3 0 0 % on a day when the speed of sound is 331 m/s?

Q5:

Two eagles fly directly toward one another, the larger eagle at a speed of 15.0 m/s and the smaller one at a speed of 20.0 m/s. Both eagles screech, the larger emitting a screech of frequency of 3 2 0 0 Hz and the smaller one emitting a screech of frequency 3 8 0 0 Hz. The speed of sound in the air around the eagles is 330 m/s.

What is the frequency of the screech heard by the larger eagle?

What is the frequency of the screech heard by the smaller eagle?

Q6:

Two cars have horns and each horn’s frequency is 800 Hz. The cars move toward one another, both sounding their horns. Car A is moving at 65.00 mph and Car B is at 75.00 mph. Use a value of 343 m/s for the speed of sound.

What is the beat frequency heard by Car A’s driver?

What is the beat frequency heard by Car B’s driver?

Q7:

Two students, 𝐴 and 𝐵 , are running in a straight line with student 𝐴 behind student 𝐵 . Student 𝐴 is carrying a tuning fork vibrating at 1 0 2 4 Hz and student 𝐵 is carrying a tuning fork vibrating at 888 Hz. Student 𝐴 is running at speed 𝑣 = 7 . 0 0 / 𝐴 m s and student 𝐵 at speed 𝑣 = 8 . 0 0 / 𝐵 m s . The speed of sound in the region around the students is 345.00 m/s.

What is the beat frequency heard by student 𝐴 ?

What is the beat frequency heard by student 𝐵 ?

Q8:

Student A runs down the hallway of the school at a speed of 8.00 m/s toward a concrete wall carrying a vibrating tuning fork of frequency 1 2 8 0 Hz. Student B stands at rest at the wall. The speed of sound in the region around the students is 345 m/s.

What is the frequency of the sound waves emanating from the tuning fork heard by student B?

What is the beat frequency heard by student A due to the interference of the sound waves emanating from the tuning fork and the sound waves reflected from the concrete wall?

Q9:

A stationary observer hears a sound that he measures to have a frequency of 1 0 0 0 Hz while the sound’s source approaches and a frequency of 850 Hz while the sound’s source recedes. The sound’s source moves relative to the observer in a straight line and at a constant speed of 75 mph. What is the temperature of the air that the sound propagates through?

Q10:

You moved a tuning fork toward you at 5.00 m/s on a day when the speed of sound was 340 m/s. What is the ratio of the frequency of the sound waves you perceived emanating from the moving tuning fork to that of the sound waves perceived when it was stationary?

Q11:

The frequency of the siren of an ambulance that is approaching you is 940 Hz. You are standing on a corner and observing a frequency of 1 0 0 0 Hz. What is the speed of the ambulance if the speed of sound is 𝑣 = 3 4 3 m/s?

Q12:

A spectator at a parade perceives a tone with a frequency of 685 Hz from an approaching trumpeter. The trumpeter is playing a note with a 678 Hz frequency. Find the speed that the musician approaches the spectator at. Use a value of 338 m/s for the speed of sound.

Q13:

Early Doppler shift experiments were conducted using a band playing music on a train. The trumpet player on a moving flatcar plays a 0.305 kHz frequency note. The sound waves heard by a stationary observer on the platform have a frequency of 0.350 kHz. What is the flatcar’s speed if the temperature of the air is 2 7 . 5 ∘ C ?

Q14:

A person watches an ambulance moving toward them at 110 km/h. The ambulance siren makes a steady 800-Hz sound.

What frequency sound does the person hear as the ambulance approaches them?

The ambulance passes the person and continues at the same speed. What frequency sound does the person hear as the ambulance recedes from them?

Q15:

At an air show, a jet flies directly toward a crowd of people at a speed of 1 0 3 1 km/h emitting a frequency of 3 8 2 1 Hz on a day when the speed of sound is 342 m/s.

What is the frequency of the sound perceived by the people in the crowd?

What is the frequency of the sound that the crowd perceives as the jet flies directly away from them?

Q16:

A galaxy moving away from Earth has a speed of 110 km/s and emits 501 nm light that is characteristic of doubly ionized oxygen. What wavelength would we observe on Earth? Give your answer to 5 significant figures.

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