At a factory, a noon whistle is sounding with a frequency of 480 Hz. As a car traveling at 85 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in frequency ff − fi heard by the driver? (Assume a temperature of 20° C.)

Question

At a factory, a noon whistle is sounding with a frequency of 480 Hz. As a car traveling at 85 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in frequency ff − fi heard by the driver? (Assume a temperature of 20° C.)

I tried this , but its wrong
[2(343)(22.22) / ((343)² - (22.22)²)] (480)= 62.27 Hz

COuld someone help me out please.

Answer 1

The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

f1=f(o)•(1+v/V),
f2=f(o)•(1-v/V),
v = 85 km/h = 23.61 m/s,
V =343 m/s,
Δf =f1-f2 = f(o)•(1+v/V)-f(o)•(1-v/V)= =2•f(o)•(v/V) =
= 2•480•23.61/343 =66.08 Hz

Answer 2

I cant solve this can someone help me please

Answer 3

To determine the change in frequency heard by the driver as they approach and then drive past the factory, we can use the Doppler effect equation. The formula for the Doppler effect in frequency is given as:

f' = f((v + vd) / (v + vs))

Where:
f' is the observed frequency,
f is the source frequency (in this case, the whistle frequency),
v is the speed of sound in air (approximately 343 m/s at 20°C),
vd is the velocity of the detector (in this case, the car),
vs is the velocity of the source (in this case, the whistle).

Step 1: Convert the car's speed to m/s
Given that the car's speed is 85 km/h, we need to convert it to m/s. 1 km/h is equivalent to 0.2778 m/s, so:

vd = 85 km/h * 0.2778 m/s
vd = 23.61 m/s (approx.)

Step 2: Calculate the observed frequency while approaching
The driver hears the whistle at frequency fi as they approach the factory, so we'll use the formula:

fi = f((v + vd) / (v + vs))

Substituting the known values:
fi = 480 Hz * ((343 m/s + 23.61 m/s) / (343 m/s - 0 m/s))

Step 3: Calculate the observed frequency while driving past
Similarly, when the car is driving past the factory, the driver hears frequency ff. We'll use the same formula, but this time substitute vd with -vd (since the car is now moving away from the source):

ff = f((v - vd) / (v + vs))

Substituting the known values:
ff = 480 Hz * ((343 m/s - 23.61 m/s) / (343 m/s + 0 m/s))

Step 4: Calculate the change in frequency
The change in frequency is given by:

Δf = ff - fi

Substituting the calculated values of ff and fi, you can find the change in frequency heard by the driver.