A police car moving at 41 m/s is initially behind a truck moving in the same direction at 17 m/s. The natural frequency of the car's siren is 800 Hz.
The change in frequency observed by the truck driver as the car overtakes him is __(Hz)
Take the speed of sound to be 340m/s.
f' = Frequency Perceived (by Truck Driver)
f0 = Natural Frequency
v = Speed of Sound
vs = Speed of Source (Police Car)
vd = Speed of Detector (Truck Driver)
f' before = f0 * [ (v-vd) / (v-vs) ] = 800Hz [ (340-17 m/s) / (340-41m/s) ] = 864.21 Hz
f' after = f0 * [ (v+vd) / (v+vs) ] = 800Hz [ (340+17m/s) / (340+41m/s) ] = 749.61 Hz
Change = | f' before - f' after | = 114.61 Hz
Hope this helps.
Well, well, well, looks like we have a speedster situation on our hands! Let's crunch some numbers and find out that change in frequency, shall we?
The change in frequency observed by the truck driver is due to the Doppler effect. Now, the formula for that is as follows:
Δf = (f_source * v_receiver) / v_sound
In this case, the source is the police car, the receiver is the truck driver, and v_sound is the speed of sound, which is 340 m/s. Now, for the fun part, plugging in the values:
Δf = (800 Hz * 17 m/s) / 340 m/s
Δf = 40 Hz
So, my mathematically inclined friend, the change in frequency observed by the truck driver as the car overtakes him is a whopping 40 Hz! That's either a police car with some serious bass or a good ol' fashion Doppler effect at work. Keep an ear out for those speedy sirens!
To find the change in frequency observed by the truck driver as the police car overtakes him, we need to use the formula for the Doppler effect:
Δf = (f * v) / (v - u)
Where:
Δf = change in frequency observed by the truck driver
f = natural frequency of the car's siren = 800 Hz
v = speed of sound = 340 m/s
u = speed of the truck = 17 m/s
Plugging in the values into the formula:
Δf = (800 * 340) / (340 - 17)
= 272000 / 323
≈ 842.00 Hz
Therefore, the change in frequency observed by the truck driver as the car overtakes him is approximately 842 Hz.
To find the change in frequency observed by the truck driver, we need to use the concept of the Doppler effect. The Doppler effect describes the change in frequency of a wave (sound or light) due to relative motion between the source of the wave and the observer.
In this case, the observer is the truck driver, and the source is the police car's siren. The frequency of the siren, as detected by the truck driver, will change due to the relative motion between the two.
The formula to calculate the observed frequency (f') is:
f' = f (v + vo) / (v + vs)
where:
f = frequency of the source (800 Hz)
v = speed of sound (340 m/s)
vo = velocity of the observer (truck) relative to the medium (same direction as the car, so 17 m/s)
vs = velocity of the source (car) relative to the medium (41 m/s)
Substituting the given values into the equation, we get:
f' = 800 (340 + 17) / (340 + 41)
Calculating this expression will give us the change in frequency observed by the truck driver.
Fd = (Vs+Vd)/(Vs-Vp) * Fp.
Fd = (343+17)/(343-41) * 800. = 953.6 Hz. = Freq. heard by driver of the truck.
Change = 953.6 - 800 = 153.6 Hz.