A police car sounding a siren with a frequency of 1580 Hz is...

A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km$/$h. ($a$) What frequencies does an observer standing next to the road hear as the car approaches and as it recedes? ($b$) What frequencies are heard in a car traveling at 90.0 km$/$h in the opposite direction before and after passing the police car? ($c$) The police car passes a car traveling in the same direction at 80.0 km$?$h. What two frequencies are heard in this car?

Key Concepts

Speed of Sound

The speed of sound in the medium (usually air) is a critical parameter in calculating Doppler shifts. It represents the speed at which sound waves propagate and is used as a reference in the Doppler equations. Realistic calculations often assume a constant speed of sound, typically around 343 m/s in air at room temperature.

Frequency Shifts in Different Scenarios

Understanding how to apply the Doppler effect in various scenarios—whether the observer is stationary or moving, and whether the source is approaching or receding—is essential. This involves setting up the Doppler formulas correctly to determine the observed frequency in each setting, ensuring that the sign conventions for approaching and receding are properly applied.

Doppler Effect

The Doppler effect describes the change in frequency or wavelength of waves as perceived by an observer moving relative to the source of the waves. In the context of sound waves, when the source approaches the observer, the frequency appears higher, and when the source recedes, the frequency appears lower. This phenomenon is crucial for understanding how motion affects the sound that a stationary or moving observer perceives.

Relative Motion Between Source and Observer

This concept focuses on how the velocities of both the source and the observer influence the observed frequency. In scenarios involving moving vehicles, the effect of relative motion must be carefully considered, using appropriate formulas that account for the direction and magnitude of each velocity relative to the medium (air).

Transcript

00:03 Okay, so we have a police car sounding a siren with a frequency 1580 hertz and the speed of the police car is 120 kilometers per hour.

00:16 Now we have to find out if we have a stationary, we have a stationary observer standing next to a road.

00:29 We have to find out when the car approaches or receives.

00:34 What frequency does the observer experience so in other way how the frequency changes if the car is approaching towards him or receiving from him so first of all let's see what's given here we have the frequency which is 1580 hertz we have the velocity of the source or in our case it's the police car with the siren so it's 120 kilometers per hour and then this velocity of the sound is given or we get that from our textbook which is 343 meters per second now you see the units are not consistent so we have to make the units consistent here so we can change our kilometers per hours to meters per seconds to be consistent so let's do that and to do so what we're gonna do is we try to get rid of our kilometers per hour unit so if we multiply one meter per second on top and put 3 .6 kilometers per hour at the bottom so this is basically same as one meter per seconds because in an hour is equal to 360s seconds so that's why you have 3 .6 kilometers per hour which is when you divide these guys you get rid of the number and it becomes one but anyway so if we do this we we get rid of this we end up having this as our velocity of the source so we need this for the rest of our calculation so we need to remember this number so we have 33 .33 meters per second as our velocity of the source and then the velocity of the sound is 343 okay so so let's see what we need to do.

03:10 So if we look at equation 12 .2 and 12 .2b, these two equations kind of explains what happens if you are, if the observer is stationary and then the source is moving towards you or moving away from you.

03:27 So if it's moving forward, then you have this equation and if it's moving away, we have this equation.

03:33 So one important thing to remember here or one note about the sign is if the source is moving towards us or towards the observer, that means your frequency will be increasing.

03:50 So whatever frequency you have when both of the objects are stationary, it will start increasing if the source and the observer starts to start to come towards...

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