You are standing at the midpoint between two speakers, a distance D away from each. The speakers are playing the exact same sound of frequency 170 Hz in phase with each other. Describe what happens when you walk 1.5 m directly toward one of the speakers. Assume the speed of sound is 340 m/s. Also assume you can't hear any sounds except those produced by the speakers.
Group of answer choices :
You begin by hearing nothing, but the sound gets louder. Then it gets quieter again until you can't hear it anymore.
You begin by hearing nothing, but the sound gets louder. Then it gets quieter again until you can't hear it anymore. Then it gets louder again.
You begin by hearing a loud sound that gets quieter until you can't hear it anymore. Then it gets louder again until it is as loud as where you started. Then it gets quieter again until you can't hear it anymore.
You begin by hearing nothing, but the sound gets louder.
You begin by hearing a loud sound that gets quieter until you can't hear it anymore. Then it gets louder again until it is as loud as where you started.
You begin by hearing a loud sound that gets quieter until you can't hear it anymore.
https://en.wikipedia.org/wiki/Standing_wave
In the middle they are in phase and you hear loud.
period = 1/170 s
wavelength = 340 m/s* (1/170 s) = 2 meters
so we move 3/4 of a wavelength.
The standing wave is of form
2 A cos 2 pi x/L * cos wt
note used cos to make max at x = 0 in middle
if x/L = 3/4
we have
2 A cos 6 pi /4* cos wt
= 2 A cos 3pi /2 * cos wt
well cos 3 pi/2 = ZERO!!!, silent there and every quarter wavelength thereafter until you hit the far wall
I mean every half wavelength until you hit the wall.
You begin by hearing nothing, but the sound gets louder. Then it gets quieter again until you can't hear it anymore.
You begin by hearing a loud sound that gets quieter until you can't hear it anymore. Then it gets louder again until it is as loud as where you started.
When you walk 1.5 m directly towards one of the speakers, you are effectively moving closer to that speaker and further away from the other speaker. As a result, the distance between you and the closer speaker decreases while the distance between you and the further speaker increases.
Since sound waves travel at a constant speed, the closer speaker's sound waves will reach you before the further speaker's sound waves. When the two sound waves meet at your location, they interfere with each other.
In this scenario, the two speakers are playing the same sound of frequency 170 Hz in phase with each other. When two sound waves of the same frequency and in phase interfere constructively, their amplitudes add up, resulting in a louder sound. Conversely, when they interfere destructively, their amplitudes cancel out, resulting in a quieter or even inaudible sound.
As you walk towards the closer speaker, the constructive interference between the two sound waves initially amplifies the sound you hear, making it louder. However, as you continue to move closer to the closer speaker, the difference in distance between the two speakers and your location increases. This leads to a phase difference between the sound waves, causing destructive interference. The amplitude of the sound decreases, and it gets quieter until you can no longer hear it.
Once you pass the point of maximum destructive interference, you start moving towards the further speaker. Now, the distance between the further speaker and your location decreases, while the distance between the closer speaker and your location increases. This change in distance results in a phase difference that leads to constructive interference once again. The sound gets louder until it reaches the same loudness as where you started.
Thus, the correct answer is: You begin by hearing a loud sound that gets quieter until you can't hear it anymore. Then it gets louder again until it is as loud as where you started.