Question

One at y +1.00n and he ofher at y-O Constmacthive mee, is heard at angla the Sound Wave frm the Saines, oj what is the frequencyof thecoure het other als b stuctive inte feren eard? which und uvs Canel?

Answer 1

a] Because the distances are assumed to be large, the path difference between the waves can be taken to be:

$\Delta = dsin\theta$

1st order maxima is observed at 0.14rad = 8.02^o

so, $2sin8.02 = \lambda$

=> $\lambda = 2sin8.02 = 0.279 m$

this is the wavelength of the sound waves.

b] Frequency = c/wavelength

c = 343 m/s

so, frequency = 1229 Hz

c] Substitute the wavelength in $dsin\theta = n\lambda$ for finding angles of higher order interferences (n = 3,4,5,...)

d]

For cancellation, destructive interference must occur

$dsin\theta =\frac {\lambda}{2}$

=> $\theta =sin^{-1}\frac{\lambda}{2d} = 4\degree$

this is the smallest angle for which the waves cancel.