1. A tube, open at both ends, is cut into four shorter pieces of unequal length.

Question

1. A tube, open at both ends, is cut into four shorter pieces of unequal length. The shorter pieces have fundamental frequencies of 225, 335, 445 and 555 Hz, respectively. What was the fundamental frequency of the original tube?
2. A train has whistle that produces a sound at 470 Hz. The train is moving with a constant speed of 30 m/s. A car, starting at rest in front of the train, moves towards the train with a constant acceleration. The car reaches a maximum speed of 60 m/s before it passes by the train. What is the range of Whistle frequencies heard by a passenger in the car? (Take the velocity of sound waves in air to be 340 m/s)
3. One charge of +35.0 uc is located at position (x1,y1) = (0,32.0 cm), and two charges of -35.0 uc are located at (x2,y2) = (-32.0 cm, 0) and (x3,y3) = (32.0 cm, 0). a) What is the electric field intensity at the origin of the coordinate system. b) What is the net force experienced by the positive charge. ( k= 8.99 x 109Nm2/C2)

Explanation / Answer

f1 = 225 ; f2 = 335 ; f3 = 445 ; f4 = 555

we know for an open tube:

f = v/2L

L = v/2f

L1 = v/2f1 = v/450

L2 = v/2f2 = v/670

L3 = v/2f3 = v/890

L4 = v/2f4 = v/1110

L(total) = L1 + L2 + L3 + L4

f = v/2 L(total)

f = v/ 2 x v/2 [1/450 + 1/670 + 1/890 + 1/1110] = 174.24 Hz

Hence, f = 174.24 Hz

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