Question

Driving your Ferrari through the Italian countryside at a speedy 88 m/s, you approach an opera diva singing a high C (1,046 Hz). What note will you actually hear as you approach? (Assume a speed of sound of 340 m/s.)

Answer 1

You will hear the note E₆

Step-by-step explanation:

We know that:

Your speed = 88m/s

Original frequency = 1,046 Hz

Sound speed = 340 m/s

The Doppler effect says that:

`f' = (v \pm v0 )/(v \mp vs)*f`

Where:

f = original frequency

f' = new frequency

v = velocity of the sound wave

v0 = your velocity

vs = velocity of the source, in this case, the source is the diva, we assume that she does not move, so vs = 0.

Replacing the values that we know in the equation we have:

`f' = (340 m/s + 88m/s)/(340 m/s) *1,046 Hz = 1,316.73 Hz`

This frequency is close to the note E₆ (1,318.5 Hz)