Respuesta :
Answer:
x = 6.25 m , x = 3.90 m , x = 1.55 m
Explanation:
given,
frequency of tone = 73 Hz
speed of sound = 343 m/s
distance between the speaker = 7.80 m
wavelength (λ) = [tex]\dfrac{v}{\mu}[/tex]
= [tex]\dfrac{343}{73}[/tex]
= 4.7 m
let the distance from speaker A be x
distance from speaker B be 7.80 - x
distance of the first point from speaker A
x - (7.80 - x) = one wavelength
2x - 7.80 = 4.7
x = 6.25 m
distance of the second point from speaker A
x - (7.80 - x) = zero wavelength
2x - 7.80 = 0
x = 3.90 m
distance of the second point from speaker A
(7.80 -x) - x = one wavelength
7.80 - 2x = 4.7
x = 1.55 m
Answer:
The distances of these three points from speaker A are 6.25 m, 3.9 m and 1.55 m.
Explanation:
Given that,
Distance = 7.80 m
Frequency f = 73.0 Hz
Speed of sound = 343 m/s
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{343}{73.0}[/tex]
[tex]\lambda=4.6986\ m[/tex]
Let the distance from speaker A is x.
The distance from speaker B is (7.80-x).
Difference between the distance must be a whole number of wavelength.
For first point,
[tex]x-(7.80-x)= \lambda[/tex]
Put the value of wavelength
[tex]2x-7.80=4.6986[/tex]
[tex]2x=4.6986+7.80[/tex]
[tex]x=\dfrac{12.4986}{2}[/tex]
[tex]x=6.25\ m[/tex]
For second point,
[tex]x-(7.80-x)= \lambda[/tex]
Put the value of wavelength
[tex]2x-7.80=0[/tex]
[tex]x=3.9\ m[/tex]
For third point,
[tex](7.80-x)-x= \lambda[/tex]
Put the value of wavelength
[tex]7.80-2x=4.6986[/tex]
[tex]-2x=4.6986-7.80[/tex]
[tex]2x=3.1014[/tex]
[tex]x=\dfrac{3.1014}{2}[/tex]
[tex]x=1.55\ m[/tex]
Hence, The distances of these three points from speaker A are 6.25 m, 3.9 m and 1.55 m.
