I rate a 100% if yoy help me! :) Thu loudspeakers ore driven by the Jome ampl,ti

Question

I rate a 100% if yoy help me! :)

Thu loudspeakers ore driven by the Jome ampl,tier and produce sound wwes uith a frequany f Take ths speed of sound in air to he small michophona is moved out Ecom point B olong o Wne perpendicuior to tho line connecthing A ard 2 a) At what, distancs con 8 will thare be destruchtue interfecene ? And constructive iner ferena2 b) TE the fnequency is made lous Enpugns there will be no posi hons olong tns tine at which deshruchive inlerferenc occuts tlow low must the frequancy be for this to be th case 2

Explanation / Answer

given two loud speakers, A and B

frequency = f

speed of sound in air = s

a. let teh distance form B where there is destructive interference be x

then

path difference = p

p = sqrt(y^2 + x^2) - x

for destructive interference

p = (2n - 1)lambda/2

hence

(2n - 1)lambda/2 = sqrt(y^2 + x^2) - x

where n = 1, 2, 3, ..

b. for there to be no location where destructive interference happens

x should not exist for n = 1 as well

hence

lambda/2 = sqrt(y^2 + x^2) - x

we can write p = y/sin(theta) - y/tan(theta)

this is a linearly increasing plot

hence, p < 0.5*lambda

hence

for n = 1

sqrt(y^2 + x^2) - x < 0.5*lambda

y/sin(theta) - y/tan(theta) < 0.5*lambda

lambda*f = c

hence

lambda= c/f

sqrt(y^2 + x^2) - x < 0.5*c/f

or

f < 0.5c/x(sqrt(y^2/x^2 + 1) - 1)

sound of ships sonar frequency, fa

speed of sound in water = u

a. wavelength emmitted by source = lambda = c/fa

b. frequency hear by whale f = (u + uw)fa/u

wavelength = c/f = uc/(u + uw)fa

hence

difference

d(lambda) = c/fa - uc/(u + uw)fa = (c/fa)(1 - u/(u + uw))

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