Two Questions with Sound Waves

1. Dec 12, 2004

Kawrae

>> A driver travels northbound on a highway at a speed of 23.0 m/s. A police car, traveling southbound at a speed of 42.0 m/s approaches with its siren sounding at a frequency of 2260 Hz.
(a) What frequency does the driver observe first as the police car approaches and then as it passes?
(b) Repeat part (a) for the case in which the police car is northbound.

I got part (a) using the formula f'=f (v+vo)/(v-vo) and f'=f (v-vo)/(v+vo), but I don't understand how to do part (b). If the police car is northbound, it would still be approaching and passing the driver... wouldn't the formulas stay the same?

>> A sound wave in air has a pressure amplitude equal to 3.94x10^-3 Pa. Calculate the displacement amplitude of the wave at a frequency of 10.3 kHz. (Note: In this section, use the following values as needed, unless otherwise specified. The equilibrium density of air is 1.20 kg/m^3; the speed of sound in air is v=343 m/s. Pressure variations are measured relative to atmospheric pressure, 1.013x10^5 Pa.)

I'm really not even sure how to start this problem... any suggestions?

Last edited: Dec 13, 2004
2. Dec 13, 2004

Gamma

Second question is a plug in problem. Every thing is given to plug in the pressure amplitude eqation P = Bk Y. Y is displacement amphlitude, B- bulk modulus = density*c^2. k is the wave number.
Regards.

3. Dec 13, 2004

Gamma

Oh in the first part, check the equation. Is it f'=f (v+vo)/(v-v'); v' = source velocity.
This equation is derived for the situation where the source and the listner are approaching each other. When using this equation, one need to be aware of the signs of vo and v'.
When the police car is south bound, source and the listner are approaching each other and the above equation is right. But when the police car is north bound, source and the listner are travelling in the same direction. Substitute -v' for v'. so you have
f'=f (v+vo)/(v+v')

4. Dec 13, 2004

Kawrae

I still don't really understand this... I can't find this formula in our book. So P would be equal to the pressure amplitude and B would be density of air times... the speed of sound squared? Would K be the frequency?

5. Dec 14, 2004

Gamma

For a sinusoidal sound waves y = Y sin (wt - kx) pressure p =- BkY Cos(wt-kx). k is the wave number 2pi/lamda. and freq*lamda = c.

For more details see Sears and Zemansky's University Physics. (I have the 5 th edition)