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Fall 2011 Homework 24 Solutions

# Fall 2011 Homework 24 Solutions - Physics 21 Fall 2011...

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Physics 21 Fall, 2011 Solution to HW-24 16-33 Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A . Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B . Both speakers emit sound waves that travel directly from the speaker to point Q . (a) What is the lowest frequency for which constructive interference occurs at point Q ? (b) What is the lowest frequency for which destructive interference occurs at point Q ? Speaker A is 3.0 m from Q , and speaker B is 1.0 m from Q , so the path difference is 2.0 m. (a) The speakers are in phase, so for constructive interference, the path difference must be an integral number of wavelengths ( ). We choose n = 1 to get the lowest frequency, so λ = 2 . 0 m. Hence λf = v f = v λ = 343 m / s 2 . 0 m = 172 Hz (b) For destructive interference the path difference must be 0.5 wavelengths. [( n + 1 2 ) λ gives destructive interference, and lowest frequency is from n = 0.] Hence take λ = 4 . 00 m and f = v λ = 343 m / s 4 . 0 m = 86 Hz 16-70 Two identical loudspeakers driven by the same am- plifier are located at points A and B , 2.00 m apart. The frequency is 784 Hz and the speed of sound in air is 344 m/s. A small microphone is moved out from point

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Fall 2011 Homework 24 Solutions - Physics 21 Fall 2011...

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