explain points SerP5E9 18 P.008 WI. My Notes Ask Your Teache Two identical louds

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points SerP5E9 18 P.008 WI. My Notes Ask Your Teache Two identical loudspeakers are placed on a wall 3.00 im apart. A listener stands 00 m from the wall directly in front of one of the speakers. A single oscillator is driving the speakers at a frequency of 300 Hz. (a) what is the phase difference in radians between the waves from the speakers when they reach the observen? Your answer should be between 0 and 2m.) rad (b) what is the frequency closest to 30 Hz to which the oscillator may be adjusted such that the observer hears sound? iHz

Explanation / Answer

1.

a) Use below figure,

L2= sqrt( L1^2 – d^2 ) = sqrt(5^2 - 3^2) = 4

Path difference , L= L2- L1 = 4 - 3 = 1m

Wavelength , = v/ f= 343/300 = 1.143m

Phase difference = (2/)*path difference = [(2*)/1.143]*1 = 1.75 rad

b) For destructive inference,

L = 0.5

= L/0.5 = 1/0.5 = 2m

f= v/ = 343/2 = 171.5Hz

2.

The wave travelling in the positive x direction

y(x,t) = Asin(wt - kx + ) -------------(1)

L= 4 => = L/4 = 6.4/4 = 1.6m

k= 2/ = (2*3.14)/1.6 = 3.925 m^-1

A=14.0cm/2 = 7.0cm= 0.07m

f= 40.0Hz => w= 2f= 2*3.14*40 = 251.2 rad/s

= 0 rad

Plugging values in (1),

y(x,t) = 0.07sin(251.2 t - 3.925x)

b)

P=0.5w2A2v -----------------(2)

= mass/length = 0.180kg/6.4m = 0.028 kg/m

v= w/k = 251.2/3.925 = 64m/s

Plugging values in (2),

P= 0.5*0.028*251.2^2*0.07^2*64 = 277 W

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