Question

A naval engineer is testing an nonreflective coating for submarines that would help them avoid detection by producing destructive interference for sonar waves that have a frequency of 512 Hz and travel at 1390 m/s. If there is a phase change for waves reflected from both the top and bottom surfaces of the coating, what is the minimum thickness of the coating? For sonar waves let nwater=1.00 and ncoating=13.5. Express your answer to three significant figures and include appropriate units.

Answer 1

Answer:

5 cm .

Explanation:

Wave length of sonar waves λ = 1390 / 512

= 2.715 m

For waves getting reflected from both layers of the coating ,  undergoing phase reversal , net change will be zero .

For destructive interference

path diff = ( 2n+1) λ / 2

2μt =  ( 2n+1) λ / 2

2 x 13.5 x t =  ( 2n+1) λ / 2

for minimum thickness

n = 0

2 x 13.5 x t = λ / 2

2 x 13.5 x t =  λ / 2

t = λ / (2 x 27)

= 2.715 / 2 x 27

= .05 m

5 cm .

Answer 2

The minimum thickness of the coating is : 5 cm

Determine the minimum thickness of the coating

Wavelength of sonar waves = 1390 / 512 = 2.715 m

Considering a destructive interference

Path difference ;

2μt =  ( 2n+1 ) λ / 2

2 * 13.5 * t = ( 2n+1 ) λ / 2

Considering minimum thickness

n = 0

2 * 13.5 * t = λ / 2

Therefore ;

t = λ / (2 x 27)

Hence ; t ( minimum thickness ) = 2.715 * / 2 * 27

                                                     = 0.05 m = 5 cm

Hence we can conclude that The minimum thickness of the coating is : 5 cm.

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