Respuesta :
Answer:
Explanation:
Wave length of sound from each of the speakers = 340 / 1700 = .2 m = 20 cm
Distance between first speaker and the given point = 4 m.
Distance between second speaker and the given sound
= √ 4² + 2² = √16 +4 = √20 = 4.472 m
Path difference = 4.472 - 4 = .4722 m.
Path difference / wave length = 0.4772 / 0.2 = 2.386
This is a fractional integer which is neither an odd nor an even multiple of half wavelength. Hence this point of neither a perfect constructive nor a perfect destructive interference.
Two identical loudspeakers, for a point of P has neither a constructive interference nor a perfect destructive interference.
- a) The point is something in between the point of maximum constructive interference and point of perfect destructive interference.
- b) The path-length difference 4.472 meters.
- c)The wavelength of the sound waves emitted by the speakers 0.2 meters.
What is interference?
Interference is the total effect of the combination of two or more waves, which form resultant wave of greater or lower amplitude.
- When the peaks of these two waves added together to form resultant wave of greater amplitude, then it is called the constructive interference.
- When the peaks of these two waves subtract together to form resultant wave of lower amplitude, then it is called the destructive interference.
The distance between the two loud speaker is 2 meters.
As he frequency of the sound wave of loudspeakers is 1700-Hz and the speed of sound is 340 m/s. Thus the wavelength can be given as,
[tex]\lambda =\dfrac{340}{1700}\\\lambda=0.2\rm m[/tex]
- a) The point of intersection of sound-
As the distance between the speaker and point is 4 meters as shown in the figure below.
Thus, the distance between the speaker 2 and the point can be find out using the Pythagoras theorem. Let this distance is (x) meters, therefore,
[tex]x=\sqrt{4^2+2^2}\\x=\sqrt{20}\\x=4.472\rm m[/tex]
Now the path difference is,
[tex]\rm PD=4.472-4\\PD=0.472[/tex]
Now the path difference can be given as,
[tex]\rm PD=\lambda\times m[/tex]
The symbol [tex]\lambda[/tex] is the wavelength where, m=1,2,3,4.... (whole number)
Put the values in above formula as,
[tex]\rm 0.4772=0.2\times m\\m=2.386[/tex]
As the value of m is not in the whole number. Thus the point is something in between the point of maximum constructive interference and point of perfect destructive interference.
- b) The path-length difference-
As the distance between the speaker and point is 4 meters as shown in the figure below.
Thus, the distance between the speaker 2 and the point can be find out using the Pythagoras theorem. Let this distance is (x) meters, therefore,
[tex]x=\sqrt{4^2+2^2}\\x=\sqrt{20}\\x=4.472\rm m[/tex]
- c)The wavelength of the sound waves emitted by the speakers-
As he frequency of the sound wave of loudspeakers is 1700-Hz and the speed of sound is 340 m/s. Thus the wavelength can be given as,
[tex]\lambda =\dfrac{340}{1700}\\\lambda=0.2\rm m[/tex]
Two identical loudspeakers, for a point of P has neither a constructive interference nor a perfect destructive interference.
- a) The point is something in between the point of maximum constructive interference and point of perfect destructive interference.
- b) The path-length difference 4.472 meters.
- c)The wavelength of the sound waves emitted by the speakers 0.2 meters.
Learn more about the interference here;
https://brainly.com/question/15967698
