a) A glass tube is open at one end and closed at the other by a movable piston.
ID: 2026358 • Letter: A
Question
a) A glass tube is open at one end and closed at the other by a movable piston. The tube is filled with air warmer than that at room temperature, and a 384-Hz tuning fork is held at the open end. Resonance is heard when the piston is 22.8 cm from the open end and again when it is 68.3 cm from the open end.(1) What speed of sound is implied by these data?
(2) How far from the open end will the piston be when the next resonance is heard?
b)
Two speakers are driven by a common oscillator at 800 Hz and face each other at a distance of 1.25 m. Locate the points along a line joining the two speakers where relative minima of sound pressure would be expected. (Use v = 343 m/s.)
ANSWER: At 0.089 1 m, 0.303 m, 0.518 m, 0.732 m, 0.947 m, and 1.16 m from one speaker
How to get the answer??????? How to explain it ???
Explanation / Answer
f = 384-Hz, L1 = 22.8 cm, L2 = 68.3 cm.
(1) What speed of sound v is implied by these data?
L = (2n + 1)/4,
v = f = 4fL/(2n + 1)
so L/(2n + 1) = constant
L1/(2n1 + 1) = L2/(2n2 + 1)
(2n1 + 1)/(2n2 + 1) = L1/L2 = 22.8/68.3 1/3, so n1 = 0, n2 = 1
v = 4fL1/(2n1 + 1) = 350 m/s
(2) How far from the open end will the piston be when the next resonance is heard?
L1/(2n1 + 1) = L3/(2n3 + 1)
22.8/1 = L3/(2*2 + 1), L3 = 114 cm
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