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Shown below is a stationary source and moving observers. Describe the frequencies observed by the observers for this configuration.
Prior to 1980, conventional radar was used by weather forecasters. In the 1960s, weather forecasters began to experiment with Doppler radar. What do you think is the advantage of using Doppler radar?
Doppler radar can not only detect the distance to a storm, but also the speed and direction at which the storm is traveling.
(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?
a. 878 Hz; b. 735 Hz
(a) At an air show a jet flies directly toward the stands at a speed of 1200 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s. What frequency is received by the observers? (b) What frequency do they receive as the plane flies directly away from them?
What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s.
$3.79\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{Hz}$
A spectator at a parade receives an 888-Hz tone from an oncoming trumpeter who is playing an 880-Hz note. At what speed is the musician approaching if the speed of sound is 338 m/s?
A commuter train blows its 200-Hz horn as it approaches a crossing. The speed of sound is 335 m/s. (a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train? (b) What frequency does the observer receive as the train moves away?
a. 12.9 m/s; b. 193 Hz
Can you perceive the shift in frequency produced when you pull a tuning fork toward you at 10.0 m/s on a day when the speed of sound is 344 m/s? To answer this question, calculate the factor by which the frequency shifts and see if it is greater than 0.300%.
Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?
The first eagle hears $4.23\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{Hz}.$ The second eagle hears $3.56\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{Hz}.$
Student A runs down the hallway of the school at a speed of ${v}_{\text{o}}=5.00\phantom{\rule{0.2em}{0ex}}\text{m/s,}$ carrying a ringing 1024.00-Hz tuning fork toward a concrete wall. The speed of sound is $v=343.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$ Student B stands at rest at the wall. (a) What is the frequency heard by student B ? (b) What is the beat frequency heard by student A ?
An ambulance with a siren $\left(f=1.00\text{kHz}\right)$ 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 ${v}_{o}=7.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$ What frequency does the nurse observe? Assume the speed of sound is $v=343.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$
$\begin{array}{}\\ \\ {v}_{\text{s}}=31.29\phantom{\rule{0.2em}{0ex}}\text{m/s}\hfill \\ {f}_{\text{o}}=1.12\phantom{\rule{0.2em}{0ex}}\text{kHz}\hfill \end{array}$
The frequency of the siren of an ambulance is 900 Hz and is approaching you. You are standing on a corner and observe a frequency of 960 Hz. What is the speed of the ambulance (in mph) if the speed of sound is $v=340.00\phantom{\rule{0.2em}{0ex}}\text{m/s?}$
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 $0.300\text{\%}$ on a day when the speed of sound is 331 m/s?
An audible shift occurs when $\frac{{f}_{\text{obs}}}{{f}_{\text{s}}}\ge 1.003$ ; $\begin{array}{}\\ \\ {f}_{\text{obs}}={f}_{\text{s}}\frac{v}{v-{v}_{\text{s}}}\Rightarrow \frac{{f}_{\text{obs}}}{{f}_{\text{s}}}=\frac{v}{v-{v}_{\text{s}}}\Rightarrow \hfill \\ {v}_{\text{s}}=0.990\phantom{\rule{0.2em}{0ex}}\text{m/s}\hfill \end{array}$
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