Two Questions with Sound Waves

In summary: P =- BkY Cos(wt-kx). k is the wave number 2pi/lamda. and freq*lamda = c. 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. In summary, the police car passes the driver at a frequency of 2260 Hz.
  • #1
Kawrae
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0
>> 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?
 
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  • #2
Second question is a plug in problem. Every thing is given to plug in the pressure amplitude equation P = Bk Y. Y is displacement amphlitude, B- bulk modulus = density*c^2. k is the wave number.
Regards.
 
  • #3
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 traveling in the same direction. Substitute -v' for v'. so you have
f'=f (v+vo)/(v+v')
 
  • #4
Gamma said:
Second question is a plug in problem. Every thing is given to plug in the pressure amplitude equation P = Bk Y. Y is displacement amphlitude, B- bulk modulus = density*c^2. k is the wave number.
Regards.

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? :cry:
 
  • #5
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)
 

1. How do sound waves travel?

Sound waves travel through a medium, such as air, by causing particles in the medium to vibrate. These vibrations create a chain reaction, with each particle passing the energy to the next one, and eventually reaching our ears as sound.

2. What is the speed of sound?

The speed of sound varies depending on the medium it travels through. In dry air at room temperature, sound travels at approximately 343 meters per second or 767 miles per hour.

3. How does the frequency of a sound wave affect its pitch?

The frequency of a sound wave directly affects its pitch. Higher frequency waves have a higher pitch, while lower frequency waves have a lower pitch. This is because the faster vibrations of high frequency waves create a higher pitch, while slower vibrations of low frequency waves create a lower pitch.

4. Can sound waves travel through a vacuum?

No, sound waves cannot travel through a vacuum because there are no particles for the vibrations to pass through. This is why sound cannot be heard in space.

5. How are sound waves measured?

Sound waves are measured using a unit called Hertz (Hz), which represents the number of vibrations per second. The higher the frequency of a sound wave, the higher the number of Hertz. The amplitude of a sound wave, or its height, is measured in decibels (dB).

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