In the figure, suppose that the separation between speakers A and B is 5.90 m an
ID: 2269463 • Letter: I
Question
In the figure, suppose that the separation between speakers A and B is 5.90 m and the speakers are vibrating in phase. They are playing identical 110-Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and the observer at C, such that he observes destructive interference?
m
Explanation / Answer
Let A, B and C create a right-angled triangle with respective sides a, b and c (b being the hypotenuse)
we can thus get the largest possible distance between speaker B and observer C by subtracting the half of wavelength (to create destructive interference) from the length of hypotenuse:
?=v/f, where v stands for the speed of sound, f for the frequency and ? for the wavelength
?=343/110; ?=3.12m
b = a^2+c^2
a^2+c^2 = (a + ?/2)^2
c=5.9m
a=10.38
then, the largest possible distance is 10.38m
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.