After giving an intense performance, a confused and disoriented ﬂautist has wandered onto the motorway! They are playing a constant 300 Hz tone on their ﬂute and are essentially stationary. If you are driving along the motorway at 100 km h-1 (27.8 m s-1), what is the frequency you hear from the ﬂautist's instrument before you pass them? (cair = 343 m s-1.)

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Physics

Guest

24 February, 19:31

After giving an intense performance, a confused and disoriented ﬂautist has wandered onto the motorway! They are playing a constant 300 Hz tone on their ﬂute and are essentially stationary. If you are driving along the motorway at 100 km h-1 (27.8 m s-1), what is the frequency you hear from the ﬂautist's instrument before you pass them? (cair = 343 m s-1.)

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Brice Pearson · Answer 1

This is a Doppler effect. Generally, if you move to a frequency source, you would detect an increase in frequency and when you move away from a source you would detect a decrease.

For this question, before you pass them, you are actually approaching them, so you would hear a higher frequency than the constant 300 Hz they are playing at.

Using the condensed formula:

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

Where: vd = Velocity of the detector.

vs = Velocity of the frequency source.

v = Velocity of sound in air.

f ' = Apparent frequency.

f = Frequency of source.

v = 343 m/s, vd = detector = 27.8 m/s, vs = velocity of the source = 0. (the flautists are not moving).

f = 300 Hz.

There would be an overall increase in frequency, so we maintain a plus at the numerator and a minus at the denominator.

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

f ' = ((343 + 27.8) / (343 - 0)) * 300

= (370.8/343) * 300 = 324.3

Therefore frequency before passing them = 324.3 Hz.

Cheers.