18. Waves & Sound

A police radar gun used to measure the speed of cars emits an electromagnetic wave (a radio wave) with a frequency of $24\text{GHz}.$ In an area where the speed limit is $30\text{ m/s},$ what should be the shift in the frequency of the wave after reflecting off traffic that is exactly following the speed limit, driving toward the police officer?

As you stand beside the road singing a lovely $450\mathrm{Hz}$ note, your friend, Lisa, drives toward you at $26\mathrm{m}/\mathrm{s}$. What frequency does Lisa hear as she listens to you croon?

The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0° with its direction of motion. The speed of sound at this altitude is 331 m>s. (a) What is the Mach number of the shuttle at this instant

The siren of a fire engine that is driving northward at 30.0 m>s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m>s. (b) What wavelength would this driver measure for these reflected sound waves?

The siren of a fire engine that is driving northward at 30.0 m>s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m>s. (a) What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck?

A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m>s and(b) receding from the first?

A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m>s and (a) approaching the first

An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 2¹/² = 1.059. With what speed must the bat fly toward the singer?

A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?

A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?

A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. a. What frequency do you hear?

BIO Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb. a. Consider an object moving at speed vo toward an at-rest source that is emitting sound waves of frequency f0 . Show that the reflected wave (i.e., the echo) that returns to the source has a Doppler-shifted frequency fecho = (v+v0 / v-vo) fo where v is the speed of sound in the medium.