An ambulance is approaching at 80 mph (35.8 m/s). If the siren produces a continuous 400 Hz tone, what frequency do you hear? Assume the speed of sound to be 340 m/s.

To calculate the frequency you hear, we need to consider the Doppler effect.

The Doppler effect describes the change in frequency of a wave (in this case, sound) due to the relative motion between the source of the wave (the ambulance) and the observer (you).

The formula for calculating the observed frequency (f') in this situation is:

f' = f * (v + v0) / (v + vs)

Where:
f' is the observed frequency
f is the actual frequency of the siren (400 Hz)
v is the speed of sound (340 m/s)
v0 is the velocity of the observer (you), assumed to be 0 m/s since you are stationary
vs is the velocity of the source (the ambulance) (35.8 m/s)

Let's substitute the values into the formula:
f' = 400 * (340 + 0) / (340 + 35.8)

Simplifying:
f' = 400 * (340 / 375.8)

Calculating the value:
f' ≈ 362.09 Hz

Therefore, the frequency you hear from the ambulance siren is approximately 362.09 Hz.

To find the frequency that you hear from the siren of the approaching ambulance, you need to consider the Doppler effect. The Doppler effect refers to the change in frequency of a sound wave due to the relative motion between the source of the sound and the observer.

The formula for the observed frequency (f) due to the Doppler effect is given by:

f = [(v + vd) / v] * fs,

where:
- f is the observed frequency,
- v is the speed of sound,
- vd is the velocity of the detector (the observer), and
- fs is the source frequency.

In this case, the speed of sound (v) is given as 340 m/s, and the source frequency (fs) is given as 400 Hz. The ambulance is approaching, so the observer's velocity (vd) will be positive and equal to 35.8 m/s (converted from 80 mph).

Plugging in the values, we can calculate the observed frequency (f):

f = [(340 + 35.8) / 340] * 400,
f = (375.8 / 340) * 400,
f = 1.105 * 400,
f ≈ 442 Hz.

Therefore, the frequency that you would hear from the siren of the approaching ambulance is approximately 442 Hz.