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Out of Phase Sound Waves

  • #1

Homework Statement


A pair of die-hard sports fans decide to ride their motorcycle to the local game, equipped with identical air horns. While stuck at a stoplight, one rider blasts his horn, emmiting a coninuous sound at a frequency of 10 rads/sec. The second rider waits just the right amount of time before also blasting his horn, so that the two sound waves are exactly π/6 radians out of phase (you can take the speed of sound in air to be v = 343 m/s, and the density of air to be 1.2 kg/m3).

a) If the sound level of each horn is 100 dB, what is the intensity of the total sound from the two horns? Express your answer as a numerical value in units W/m2.

b) If the light turns green and the bike then speeds off at 100 m/s with the horns still blaring, what apparent frequency is heard by a person left standing by the intersection?

Homework Equations


Sound level=10log (I/(10^/12))

The Attempt at a Solution


To start, I figure I have to calculate the intensity of each horn and, if I use the equation above, it comes out to I=10^-2 w/m^2. Because the horns are out of phase by π/6 but have the same frequency, I know that complex wave is created, so I don't think the intensity would just double. How do I calculate the difference in intensity resulting from the phase change?
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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You need to add the two waves together ... this is done by vector addition of the phasors.

Note: for the purposes of the problem the wave is just another sine wave - not all that complicated at all - though IRL this would be quite hard to set up.
You are expected to assume the bikers are close enough together that diffraction effects are small.
 

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