Respuesta :
Answer:
a) f = 453.3Hz
b) f = 443.1Hz
c) f = 420Hz
Explanation:
First of all we need to know the positions and velocities of both vehicles.
For the car:
Xc(-5) = 0m; Vc(-5) = 0m/s
[tex]Xc(5) = 2.5*5^2/2=31.25m[/tex]; Vc(5)=2.5*5 = 12.5m/s
[tex]Xc(10)=2.5*10^2/2=125m[/tex]; Vc(10)=2.5*10=25m/s
For the truck:
Xt(-5)=10*(-5) = -50m; Vt(5)=10m/s
Xt(5)=10*5 = 50m; Vt(5)=10m/s
Xt(10)=10*10=100m; Vt(10)=10m/s
Now for part a) t=-5s. The truck is behind the car, so:
[tex]f=\frac{C}{C-Vt}*fo = 453.3Hz[/tex]
Now for part b) t=5s. The car is behind the truck, so:
[tex]f=\frac{C+Vc}{C+Vt}*fo = 443.1Hz[/tex]
Now for part b) t=10s. The truck is behind the car, so:
[tex]f=\frac{C-Vc}{C-Vt}*fo = 420Hz[/tex]
Doppler effect is used to find the change in wave frequency when either the observer or source or both are moving
(a) 5 seconds before the light turned green, the frequency of sound heard by the observer is 453.[tex]\overline {213}[/tex] Hz
(b) 5 seconds after the light turned green the frequency of the sound heard by the observer is approximately 443.12 Hz
(c) 10 seconds after the light turned green the frequency heard by the light is 420.[tex]\overline{180}[/tex] Hz
The reason the above values are correct is given as follows;
The given parameters are;
Initial velocity of the car = 0 (Starts from rest)
Acceleration of the car, a = 2.5 m/s²
The constant velocity of the truck that passes the car, [tex]v_s[/tex] = 10 m/s
Frequency of the sound emitted by the truck, f = 440 Hz
(a) The frequency of the sound heard by the driver of the car 5 seconds before the light turns green is given as follows;
The Doppler shift formula is given as follows;
[tex]f' = \dfrac{v }{v - v_s} \times f[/tex]
Where;
v = The speed of sound in air ≈ 343 m/s
Therefore;
[tex]f' = \dfrac{343}{343 - 10} \times 440 \approx 453.\overline{213}[/tex]
The frequency of sound heard by the observer, f' = 453.[tex]\overline {213}[/tex] Hz
(b) The speed of the car t = 5 seconds after the light turns green is given as follows;
v = u + a·t
∴ v = 0 + 2.5 × 5 = 12.5
The speed of the car, 5 seconds after the light turns green, [tex]v_0[/tex] = 12.5 m/s
The position of the car at 5 seconds after the light turns green is given as follows;
[tex]s = u\cdot t + \dfrac{1}{2} \cdot a \cdot t^2[/tex]
u = 0
[tex]\therefore s = \dfrac{1}{2} \times 2.5 \times 5^2 = 31.25[/tex]
The position of the truck after 5 seconds = 5 s × 10 m/s = 50 m
Therefore, the car is moving towards the truck, which is moving away from the car
The correct formula to use is therefore;
[tex]f' = \dfrac{v + v_0}{v + v_s} \times f[/tex]
[tex]f' = \dfrac{343 + 12.5}{343 + 10} \times 440 \approx 443.12[/tex]
The frequency of the sound heard by the driver, f' ≈ 443.12 Hz
(c) 10 seconds after the light turns green, we have;
v = 0 + 2.5 × 10 = 25
The velocity of the car = 25 m/s
The position of the car, s₁₀, is given as follows;
[tex]s_{10} = \dfrac{1}{2} \times 2.5 \times 10^2 = 125[/tex]
The position of the car, s₁₀ = 125 m
The position of the truck, d₁₀ = 10 s × 10 m/s = 100 m
Therefore, the car is ahead of the truck, and the equation to be used is therefore;
[tex]f' = \dfrac{v - v_0}{v - v_s} \times f[/tex]
Which gives;
[tex]f' = \dfrac{343 - 25}{343 - 10} \times 440 \approx 420.\overline{180}[/tex]
The frequency of the sound heard by the driver, f' = 420.[tex]\overline{180}[/tex] Hz
Learn more about the Doppler effect here:
https://brainly.com/question/15097772
