Two loudspeakers 6.0m apart are playing the same frequency. If you stand 14.0m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 14.0m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakersIf you stay 14.0m directly in front of one of the speakers, for what other frequencies between 100Hz and 800Hz is there a minimum sound intensity at this point?
Express your answer numerically. If there is more than one answer, enter your answers in ascending order separated by commas.
Express your answer numerically. If there is more than one answer, enter your answers in ascending order separated by commas.
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First draw a big clear diagram. You need to know the speed of sound in air under normal conditions.
When you are directly in front, between the speakers, the distance to each (which will be found using Pythagoras' theorem in a square with base 3m and height 14m) is the same, so you get constructive interference.
When you move in front of one of the speakers (so now the distance to that speaker is just 14 m, the distance to the other speaker is the hypotenuse of a triangle with base 6m and height 14m) you first get destructive interference, which means there must be a half-wavelength difference in the path differences. So calculate the difference in length between the two paths, double it and you have the wavelength of the sound.
Now that you have the wavelength, and you know the speed of sound, you can use v = f(lambda) to find the frequency.
For quiet spots (destructive interference) you need 1/2, 3/2, 5/2, 7/2 etc wavelength path differences between the paths from the two speakers to that point. Calculate the wavelengths using that information then convert them to frequencies.
I've told you *how* to do it - have a go. If you're still stuck leave a comment and I can work through an example.
When you are directly in front, between the speakers, the distance to each (which will be found using Pythagoras' theorem in a square with base 3m and height 14m) is the same, so you get constructive interference.
When you move in front of one of the speakers (so now the distance to that speaker is just 14 m, the distance to the other speaker is the hypotenuse of a triangle with base 6m and height 14m) you first get destructive interference, which means there must be a half-wavelength difference in the path differences. So calculate the difference in length between the two paths, double it and you have the wavelength of the sound.
Now that you have the wavelength, and you know the speed of sound, you can use v = f(lambda) to find the frequency.
For quiet spots (destructive interference) you need 1/2, 3/2, 5/2, 7/2 etc wavelength path differences between the paths from the two speakers to that point. Calculate the wavelengths using that information then convert them to frequencies.
I've told you *how* to do it - have a go. If you're still stuck leave a comment and I can work through an example.