Respuesta :
Answer:
L = 3.8 m
Explanation:
As we know that the frequency of sound is given as
[tex]f = 686 Hz[/tex]
speed of the sound is given as
[tex]v = 332 + 0.6 t[/tex]
[tex]v = 332 + (0.6 \times 20)[/tex]
[tex]v = 344 m/s[/tex]
now we have wavelength of sound is given as
[tex]\lambda = \frac{v}{f}[/tex]
[tex]\lambda = \frac{344}{686}[/tex]
[tex]\lambda = 0.50 m[/tex]
now we have path difference at initial position given as
[tex]\Delta L = \sqrt{L^2 + d^2} - L[/tex]
[tex]\Delta L = \sqrt{3^2 + 2.5^2} - 2.5[/tex]
[tex]\Delta L = 3.9 - 2.5 = 1.4 m[/tex]
now we know that for minimum sound intensity we have
[tex]\Delta L = \frac{2N + 1}{2}\lambda[/tex]
[tex]\Delta L = \frac{2N + 1}{2}(0.50)[/tex]
so we have
N = 2
[tex]\Delta L = 1.25 m[/tex]
so we have
[tex]\sqrt{2.5^2 + L^2} - L = 1.25[/tex]
[tex]2.5^2 + L^2 = L^2 + 1.25^2 + 2.5L[/tex]
[tex]L = 1.875 m[/tex]
Now for N = 1
[tex]\Delta L = 0.75 m[/tex]
so we have
[tex]\sqrt{2.5^2 + L^2} - L = 0.75[/tex]
[tex]2.5^2 + L^2 = L^2 + 0.75^2 + 1.5L[/tex]
[tex]L = 3.8 m[/tex]
so the next minimum intensity will be at L = 3.8 m
