A siren mounted on the roof of a firehouse emits sound at a frequency of 900 Hz. A steady wind is blowing with a speed of 15 m/s. Take the speed of sound in calm air to be 343 m/s.

(c) Firefighters are approaching the siren from various directions at 15.0
m/s. What frequency does a firefighter hear if he or she is approaching
from an upwind position, so that he or she is moving in the direction
in which the wind is blowing?

_____Hz

(d) What frequency does a firefighter hear if he or she is approaching from a downward position and moving against the wind?

I know that for part C the Observer is traveling at 0m/s with respect to the wind and for Part D the observer is moving at 30m/s with respect to the wind. I know that the speed for the source is 15m/s.

I need help figuring out why the source is traveling towards observer for part C and away for part C. I don't get the direction of the sound from the source. Basically I am having trouble with setting up the correct denominators.

To determine the frequency heard by the firefighter, we need to consider the relative motion between the source (siren) and the observer (firefighter) and how it affects the apparent frequency.

In part (c), the firefighter is approaching the siren from an upwind position, moving in the direction in which the wind is blowing. This means the firefighter and the wind are both moving towards the siren. Therefore, with respect to the siren, the observer is moving towards it at a speed of 15.0 m/s (speed of the firefighter).

To calculate the frequency heard by the firefighter (in Hz), we can use the formula for the apparent frequency (f'):

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

Where:
f' is the apparent frequency heard by the firefighter,
f is the actual frequency emitted by the siren (900 Hz),
v is the speed of sound in calm air (343 m/s),
vo is the speed of the observer (15.0 m/s),
and vs is the speed of the source (speed of the siren, 15.0 m/s).

Substituting the given values into the formula:

f' = (343 + 15.0) / (343 + 15.0) * 900
f' = 358 / 358 * 900
f' = 900 Hz

Therefore, the firefighter approaching from the upwind position will hear the same frequency of 900 Hz as emitted by the siren.

Now let's move on to part (d), where the firefighter is approaching from a downward position and moving against the wind. In this case, the firefighter and the wind are moving in opposite directions. When an observer moves towards a stationary source, approaching it, the relative motion decreases the apparent frequency. The same principle applies here.

With respect to the siren, the observer is moving away from it at a speed of 15.0 m/s (speed of the firefighter).

Using the same formula for the apparent frequency:

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

Substituting the given values:

f' = (343 - 15.0) / (343 + 15.0) * 900
f' = 328 / 358 * 900
f' = 822 Hz

Therefore, the firefighter approaching from a downward position and moving against the wind will hear a frequency of 822 Hz from the siren.

To summarize:
(c) Firefighter approaching from an upwind position hears a frequency of 900 Hz.
(d) Firefighter approaching from a downward position and moving against the wind hears a frequency of 822 Hz.