A sound wave of 50 cm and frequency 600hz calculate speed of sound ??
Answers
Solution:
The corresponding figure of the sound waves in the passing through the curve part and straight part is shown below:
Consider the sound waves start from the point A. The sound waves will meet at the point B and interfere and can be detected.
The path length of the sound waves passing through the curve is equal to half the circle having radius r centered at C.
Thus, the path length of the sound waves in the curve part is
L1 = πr
The path length of the sound in the tube ABC is equal to the diameter of the circle having radius r centered at C. So, the path length of the sound waves traveling in it is
L2 = 2r
Now, the path difference of the sound waves at the point C is
Δp = L1- L2
= πr – 2r
= (π – 2)r
For the sound to be heard minimum at the detector, the difference in path length of the sound waves is
Δp = λ/2
Insert Δp = (π – 2)r in the above equation gives
Δp = λ/2
(π – 2)r = λ/2
r = λ/[2(π-2)]
Substitute 42.0 cm forλ in the above equation gives
r = λ/[2(π-2)]
= [(42.0 cm) (10-2 m/1 cm)]/2(3.14-2)
= 18.421×10-2 m
Rounding off to three significant figures, the smallest radius of the curve part of the tube to be heard minimum sound at the detector is 18.4×10-2 m.
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