Assume you have two loudspeakers separated 1 meter excited by the same oscillator emitting an 1150 Hz sound frequency. You are 4 m from one of the loudspeakers. At what distance from you should be the second loudspeaker to produce destructive interference? Assume the air velocity is 343 m/s.
determine how many wavelengths is 4m.
Then add one half wavelength, convert that to meters. That is the answer.
so what's the answer??
Lambda = wave length, we get this by velocity / frequency (v/f)
The destructive interefrence is a point were both sound waves cancel's each other out, basically that happens when both speaker have the same oscillator, what they have, and the lambda is moved a half.
Labda = 0.3 and we know that we stay 4m away, so ad the half lambda to 4m or subtrahaet it. = 4.15m or 3.85m
Corre
* maybe it isn't correct, so if someone has the same result pls write, and about the substrate i'm not sure if this works
To determine the distance from you at which the second loudspeaker should be placed to produce destructive interference, we can use the concept of path difference.
Path difference is the difference in the distances traveled by two waves from their sources to a given point. Destructive interference occurs when the path difference between two waves is equal to an odd multiple of half a wavelength (λ/2).
First, let's find the wavelength of the sound wave emitted by the oscillator. We can use the formula:
λ = v/f
where λ is the wavelength, v is the velocity of sound in air, and f is the frequency.
Here, the frequency is 1150 Hz, and the velocity of sound in air is 343 m/s. Thus, the wavelength is:
λ = 343 m/s / 1150 Hz
≈ 0.298 m
Since we want destructive interference, the path difference should be an odd multiple of half a wavelength. So, let's say the path difference is (2n + 1) * λ/2, where n is an integer.
To find the distance from you at which the second loudspeaker should be placed, we can use the formula:
d = (2n + 1) * λ/2
where d is the distance from you to the second loudspeaker.
In this case, you are 4 meters away from the first loudspeaker. So, the path difference would be:
(2n + 1) * λ/2 = 4 m
Simplifying this equation, we get:
(2n + 1) * 0.298 m/2 = 4 m
(2n + 1) * 0.298 m = 8 m
Now, we can solve for the value of n:
2n + 1 = 8 m / 0.298 m
2n + 1 ≈ 26.85
2n ≈ 26.85 - 1
2n ≈ 25.85
n ≈ 12.93
Since n should be an integer, we can round it down to the nearest whole number, which is 12.
Finally, substituting the value of n back into the equation, we can find the distance from you to the second loudspeaker:
d = (2n + 1) * λ/2
d = (2 * 12 + 1) * 0.298 m/2
d ≈ 13.89 m
Therefore, the second loudspeaker should be placed approximately 13.89 meters away from you to produce destructive interference.