Exam 14: Mechanical Waves

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the wavelength of the sound it will produce?

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light, assuming that the light radiates uniformly in all directions.

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m². Another student is 4.0 m away from the talkers. What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption.

Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t) II: y = 0.15 sin(6x - 3t) III: y = 0.23 cos(3x + 6t) IV: y = -0.29 sin(1.5x - t) Which of these waves have the same speed?