Solve for the Speed of a Car Using Doppler Effect - Homework Question

[meeklobraca]

Homework Statement

A car speeds towards the outside wall with its horn sounding a frequency of 160 HZ. The sound waves reflected off the wall cause the driver to hear 8.0 beats per second. There is no wind and the speed of sound is 343 m/s. Find the speed of the car.

Homework Equations

The Attempt at a Solution

Well with the beats being 8, I've reckoned that the sound that the driver hears is either 152 or 168 HZ. But neither of those two frquencies lead me to the correct answer. I've thought that the frequency the driver hears should be 168 HZ because the freqquency goes up in situations like that.

What do you guys/girls think?

 

[Stonebridge]

You are correct about the beats meaning that he hears either 152 or 168 Hz reflecting back from the wall.
Don't forget, though, that the Doppler effect has influenced this value twice.
The speed of travel towards the wall has increased the frequency with which the sound waves strike the wall, and are reflected.
But the car then meets these reflected waves while, itself, traveling towards the wall.
Does this influence your result?

 

[kerimek]

Based on the given information, we can use the Doppler effect equation to solve for the speed of the car. The equation is as follows:

f = f0 * (v +/- vr) / (v +/- vs)

Where:
f is the frequency heard by the driver
f0 is the original frequency emitted by the car's horn
v is the speed of sound
vr is the speed of the receiver (in this case, the driver)
vs is the speed of the source (in this case, the car)

We know that f0 = 160 Hz, v = 343 m/s, and vr = 0 m/s (since the driver is not moving). We also know that the frequency heard by the driver is either 152 Hz or 168 Hz, depending on whether the car is moving towards or away from the driver.

If we plug in these values and solve for vs, we get:

vs = (f - f0) * v / (f + f0)

For f = 152 Hz:
vs = (152 Hz - 160 Hz) * 343 m/s / (152 Hz + 160 Hz) = -8 * 343 m/s / 312 Hz = -8.72 m/s

For f = 168 Hz:
vs = (168 Hz - 160 Hz) * 343 m/s / (168 Hz + 160 Hz) = 8 * 343 m/s / 328 Hz = 8.37 m/s

Since the car cannot have a negative speed, we can conclude that the frequency heard by the driver is 168 Hz and the speed of the car is 8.37 m/s. This means that the car is moving towards the driver at 8.37 m/s.

In conclusion, the speed of the car using the Doppler effect is 8.37 m/s.