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The width D of a diffraction horn loudspeaker is 5.00 cm. The speed of sound is...

The width D of a diffraction horn loudspeaker is 5.00 cm. The speed of sound is 343 m/s. At what frequency is the diffraction angle θ equal to 45°?

Answer: 9700Hz

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Homework Answers

Answer #1

Use the expression -

Sin(θ) = 1.22 (λ / D) ---------------------------------------(i)

Given that -

D = 5 cm = 0.05 m

θ = 45 deg

Put these values in equation (i) -

sin45 = 1.22*(λ / 0.05)

=> 0.707 = 1.22*(λ / 0.05)

=> λ = (0.707 * 0.05) / 1.22 = 0.0310 m

Therefore, the required frequency is -

f = v / λ = 343 / 0.0310 = 11064 Hz

You have mentioned the answer as 9700 Hz. The variation in the result is due to approximation of the value of variables we have considered or due to the value of speed of sound we have taken.

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