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TUTORIAL 5A: VIBRATIONS, WAVES & SOUND

1.   A tennis player uses a racket to bounce a ball up and down with a constant period. Is this a simple harmonic motion? Explain.

2.   A 1.50 kg block at rest on a frictionless tabletop is attached to a horizontal spring having constant 19.6 N/m. The spring is initially unstretched. A constant 20.0 N horizontal force is applied to the object causing the spring to stretch.

(a)        Determine the speed of the block after it has moved 0.300 m from equilibrium.

(b)        Find the frequency of the motion.

(c)         If the spring is cut in half, what happen to its displacement?

3.   A mass–spring system is in SHM in the horizontal direction. If the mass is 0.25 kg, the spring constant is 12 N/m and the amplitude is 15 cm;

a.   What would be the maximum speed of the mass?

b.   Where would this occur?

c.   What would be the speed at a half-amplitude position?

4.   Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A 5.00 m length of string with a total mass of 0.0600 kg is used.

(a) What is the required tension in the string?

(b) Calculate the wave speed in the string if the tension is 8.00 N.

5.   Given the same tension and length, will a thicker or thinner guitar string sound higher in frequency? Why?

QUESTIONS FROM TEXT BOOK

(PAGE 456 QUESTIONS NO. 49, 50, 53, 54)

49. A phone cord is 4.00 m long. The cord has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.800 s. What is the tension in the cord?

50. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.800 s to reach the opposite tower, 20.0 m away. If a 1 m length of the rope has a mass of 0.350 kg, find the tension in the tightrope.

53. Transverse waves with a speed of 50.0 m/s are to be produced on a stretched string. A 5.00 m length of string with a total mass of 0.0600 kg is used.

(a) What is the required tension in the string?

(b) Calculate the wave speed in the string if the tension is 8.00 N.

54. An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large object suspended from it. Assume a wire of mass 4.00 g is 1.60 m long and has a 3.00 kg object suspended from it. A pulse requires 36.1 ms to traverse the length of the wire. Calculate g_Moon from these data. (You may neglect the mass of the wire when

 calculating the tension in it.)

6.   Explain why sound travels faster in warmer than in colder air.