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Type of Interference and intensity level problems

1. There are two speakers at the front of the room. Each is outputting a 250Hz pure tone. For each of the following situations, will you hear constructive interference (a loud noise) or destructive interference (soft or no noise). Lambda represents the wavelength of the 250Hz tone. Choices: Constructive, Destructive.
a. You are 2.5 lambda away from speaker A; 3 lambda away from speaker B and at the speakers the waves are exactly in phase.
b. You are 3 lambda away from speaker A; 2 lambda away from speaker B and at the speakers the waves are exactly in phase.
c. You are 3 lambda away from speaker A; 2.5 lambda away from speaker B and at the speakers the waves are exactly out of phase.
d. You are 3 lambda away from speaker A; 2 lambda away from speaker B and at the speakers the waves are exactly out of phase.

2. You are standing in the middle of a large room listening to acacaphony of sounds. Rank the intensity level of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. (Remember that if you have a tie, you skip some ranks.)
a. One hundred buzzers each are producing a sound with intensity level of 73dB.
b. An object emitting a sound with an intensity of 90dB.
c. Two buzzers each are producing a sound with intensity level of 88dB.
d. Ten buzzers each are producing a sound with intensity level of 78dB.

3. You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you.
a. An object emitting a sound with an intensity of 1.0*10^5 W/m2.
b. An object emitting a sound with an intensity level of 110 dB.
c. Two buzzers each are producing a sound with intensity level of 40 dB.
d. An object emitting a sound with an intensity level of 50 dB.

4. A stereo is playing music with an output of 55 dB. If the volume is turned up so that the output intensity is 100 times greater, what will be the new intensity level?

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Solution Preview

1. First let's define what path difference is: length of the path of one wave minus length of path of other wave.
If the wave is in phase, then the path difference is whole number of wavelengths (e.g. 0 lambda, 1 lambda, 2 lambda ...) ---- ...

Solution Summary

For the interference problems, we use the path difference and its phase state (whether in or out of phase) to know the type of interference. For the intensity level problems, we use the main equation and derive some simpler equations so that we can eliminate some of the unknown variables.

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