Does the speed of sound wave change when the source velocity change? 
The speed of sound in air is about $740$ miles per hour. Suppose that a police car is sounding its siren and is driving towards you at $60$ miles per hour. At what speed is the sound of the siren approaching you?

My teacher says the answer is $720 \text{ mph}$ - is this correct? Or is the correct answer $800 \text{ mph}$?
 A: 
My teacher says the answer is $720 \text{ mph}$ - is this correct? Or is the correct answer $800 \text{ mph}$?

Neither is correct. The speed of sound in air remains at $740 \text{ mph}$.

The speed of sound in medium is constant and depends only on the type of medium. However, the sound wave frequency will change if the source and listener are moving relative to each other. This is known as the Doppler effect (see figure below)
$$f_L = \frac{v + v_L}{v + v_S} f_S$$
where $f_S$ and $f_L$ are source (emitted) and listener (observed) frequency, $v_S$ and $v_L$ are source and listener speed relative to the medium, and $v$ is sound propagation speed in the medium. You have to be careful with the signs for $v_S$ and $v_L$:

*

*$v_S$ is positive if the source is moving away from the listener, and

*$v_L$ is positive if the listener is moving towards the source.


Source: H. D. Young, R. A. Freedman, "University Physics with Modern Physics in SI Units", 15th ed., 2019.

Even if the police car is approaching you at $60 \text{ mph}$ the speed of sound in air remains at $740 \text{ mph}$. However, you will hear the siren at the following frequency
$$f_L = \frac{740 + 0}{740 - 60} f_S \approx 1.1 f_S$$
Since $f_L > f_S$ it means that you hear higher frequency than emitted, i.e. you hear peaks of the police-car siren spaced closer in time than they are emitted. When source is moving away from a stationary listener, the listener hears lower frequency than emitted.
A: The speed of sound is constant regardless of how fast the source is moving, as sound is propagated through collisions in the air, which take place independently of the source.
If YOU are moving however, then the relative speed of the sound wave is changed.
Your teacher is wrong, it's 740
