Physics question (highschool): frequency and velocity

Question

When a helicopter, whose engine emits a 186-Hz roar, flies past you at a speed of 225 km/h, you hear a drop in the pitch of the engine. If the speed of sound in air is 342 m/s, what is the change in the engine’s frequency that you hear from the time it is approaching you to the time it is moving away from you? Answer:70.3 Hz please show process of finding the answer?

Answer 1

Hi Habiba E.,

It's not so difficult, if you wave your quantities around freely. But when in doubt, follow the wavefronts!

225 km hr^-1: translate into m/s = 62.5 m s^-1

So how far does the heli move between emitting wavefronts? = 62.5 m s^-1 / 186 s^-1 = 0.33602 m

So you will be receiving wavefronts not every 342/186 = 1.83871 m, but every 1.83871-0.33602 = 1.5027 m, equivalent to 342/1.5027 = 227.59 Hz. Going away, the wavelengths are 1.83871+0.33602 = 2.17473 m, equivalent to 342/2.17473 = 157.26 Hz . The difference = 70.33 Hz.

The only tricky thing here, is remembering that distances add and subtract. In these kinds of problems, frequencies don't. In other kinds of problems (interfering sinewaves), frequencies do add and subtract. But that's an entirely different physical set-up.

--Cheers, -- Mr.d .