# Can we apply simple mechanics laws on sound waves

I made up a question to make you understand my doubt , see

Assume that a car is travelling with speed v to a wall . When car is at distance x from wall it emits a sound signal . Find time after the signal reaches the car again ? ( Speed of sound $$= v_s$$ )

Now if we think that sound wave is like an object and use relative motion than sound will approach wall with speed $$v+v_s$$ and again come to car after collision with wall with speed $$v+2v_s$$ So $$t=\frac{x}{v+v_s}+\frac{x-\frac{xv}{v+v_s} }{v+2v_s}$$

Is it expression right ? Also how will Doppler effect will affect the answer ?

Thanks for help and welcome for any edits!

Now if we think that sound wave is like an object and use relative motion than sound will approach wall with speed $$v + v_{s}$$...

No, I think you are misunderstanding something here. A linear sound wave will always propagate at the speed of sound once emitted in a homogeneous, uniform medium. If your expression were correct, how could a shock wave form? That is, the assumption that the sound wave moves at $$v + v_{s}$$ implies that it will always be faster than the emitting object, which is not true.

...and again come to car after collision with wall with speed $$v + 2 \ v_{s}$$...

This second expression is also incorrect. The sound wave would approach the car at $$v + v_{s}$$.

When car is at distance x from wall it emits a sound signal. Find time after the signal reaches the car again ?

You need to solve this in a piece-wise fashion. Start with the following:

• sound pulse emitted at $$t = 0$$ at a distance $$\Delta x_{i}$$ from the wall
• this pulse will reach the wall in $$\Delta t_{0} = v_{s} \ \Delta x_{i}$$
• at the time when this pulse hits the wall the emitting source has moved $$\Delta x_{d} = v \ \Delta t_{0}$$
• at this time, the emitting source is $$\Delta x_{r}$$ from the wall
• the final piece of time is given by $$\Delta t_{1} = \Delta x_{r} \left( v + v_{s} \right)$$

Then the answer to your question is just adding the two $$\Delta t$$'s together.

Also how will Doppler effect will affect the answer ?

The Doppler effect only changes the frequency at the receiver, not the speed of propagation.