C.5 多普勒效應：練習題

A vehicle sounding its horn moves at a constant speed towards a stationary observer. Which of the following correctly describes the observed frequency and wavelength of the sound compared to the frequency and wavelength emitted by the source?

Light from a distant galaxy is observed on Earth. A specific absorption line, which has a laboratory wavelength of \(480 \text{ nm}\), is detected at a wavelength of \(504 \text{ nm}\). Using the Doppler approximation for electromagnetic waves, what is the recession speed of the galaxy?

A police car travels at \( 35 \text{ m s}^{-1} \) while its siren emits a sound of frequency \( 1200 \text{ Hz} \). It is chasing a stolen vehicle that is traveling at \( 25 \text{ m s}^{-1} \) in the same direction. What frequency does the driver of the stolen vehicle hear? (The speed of sound in air is \( 345 \text{ m s}^{-1} \))

A source of sound emits waves of frequency \( f \) and wavelength \( \lambda \). If the source moves at a constant speed directly away from a stationary observer, what are the changes, if any, in the observed frequency and the observed wavelength compared to the source values?

A train whistle emits a sound of frequency \( 640 \text{ Hz} \). As the train approaches a stationary observer at a constant speed of \( 30.0 \text{ m s}^{-1} \), what is the frequency heard by the observer? (Take the speed of sound in air to be \( 330 \text{ m s}^{-1} \))

The hydrogen-alpha spectral line has a wavelength of \( 656.3 \text{ nm} \) in the laboratory. When observing a distant star, this line is shifted to \( 657.1 \text{ nm} \). Determine the velocity at which the star is receding from Earth, assuming the speed of light is \( 3.00 \times 10^{8} \text{ m s}^{-1} \).

A source of sound moves at a constant speed \( v_{s} \) towards a stationary reflecting surface. The source detects the sound reflected from the surface at a frequency that is \( 1.25 \) times the frequency it emits. Determine the ratio \( \frac{v_{s}}{v} \), where \( v \) is the speed of sound in the medium.

An observer moves at a speed of \(15 \text{ m s}^{-1}\) towards a stationary siren that emits a constant frequency of \(800 \text{ Hz}\). Calculate the frequency detected by the observer if the speed of sound is \(330 \text{ m s}^{-1}\).

An ambulance siren emits a sound of frequency 800 Hz. The ambulance is traveling at a constant speed of \(30 \text{ m s}^{-1}\) towards a stationary observer. The speed of sound in air is \(340 \text{ m s}^{-1}\).
(a) Calculate the frequency heard by the observer as the ambulance approaches.
(b) Calculate the frequency heard by the observer after the ambulance has passed and is moving away at the same speed.

An ultrasound medical scanner uses a stationary probe to measure the speed of blood flow in an artery. The probe emits ultrasound waves at a frequency of 5.0 MHz. The waves reflect off red blood cells moving directly away from the probe at speed \(v_b\). The speed of sound in human tissue is \(1540 \text{ m s}^{-1}\).
(a) Explain why the frequency of the wave received back at the probe is shifted twice.
(b) If the detected frequency shift (beat frequency) between the emitted and reflected waves is 1200 Hz, calculate the speed of the blood cells.