A car traveling at 22 m/s honks its horn as it directly approaches the side of a large building.The car horn plays a long sustained note with frequency f₀ = 230 Hz (in the car's frame of reference).The sound is strongly reflected off the building back to the driver.What is the frequency of the reflected wave that the driver hears? A)230 Hz B)216 Hz C)276 Hz D)262 Hz E)246 Hz

Question

Quizplus · Accepted Answer

When the sound wave reflects off the building, its frequency does not change, but its wavelength does. The reflected wave has to travel the distance the original wave traveled twice (to the building and back), so its wavelength is doubled. This means that the frequency of the reflected wave is given by:

f_reflected = f_original * (v_sound + v_car) / (v_sound - v_car)

where v_sound is the speed of sound (about 343 m/s) and v_car is the speed of the car (22 m/s, since it is approaching the building).

Plugging in the numbers, we get:

f_reflected = 230 * (343 + 22) / (343 - 22) ≈ 262 Hz

Therefore, the driver hears a reflected wave with a frequency of 262 Hz, which is choice D.

A Car Traveling at 22 M/s Honks Its Horn as It