Suppose you are stopped for a traffic light, and an ambulance approaches you from behind with a speed of 19.0 m/s. The siren on the ambulance produces sound with a frequency of 960 Hz as measured when you are at rest relative to the ambulance. The speed of sound in air is 343 m/s. What is the wavelength of the sound reaching your ears?

To find the wavelength of the sound reaching your ears, we can use the formula:

wavelength = speed of sound / frequency

First, we need to determine the speed of sound relative to you. Since you are not moving, the speed of sound relative to you is still 343 m/s.

Next, we need to determine the frequency of the sound relative to you. This can be calculated using the Doppler effect formula:

frequency observed = frequency emitted * (speed of sound + speed of observer) / (speed of sound + speed of source)

In this case, you are at rest relative to the ambulance, so your speed is 0 m/s. The frequency emitted by the siren is 960 Hz.

Plugging these values into the formula, we get:

frequency observed = 960 Hz * (343 m/s + 0 m/s) / (343 m/s + 19 m/s)

Simplifying the expression, we have:

frequency observed = 960 Hz * (343 m/s) / (362 m/s)

The frequency observed is equal to 913.26 Hz.

Now, we can calculate the wavelength by dividing the speed of sound by the frequency observed:

wavelength = 343 m/s / 913.26 Hz

Calculating this, we find:

wavelength ≈ 0.375 m

Therefore, the wavelength of the sound reaching your ears is approximately 0.375 meters.