Exam 15: Mechanical Waves

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0.It is vibrating in its third OVERTONE,and the equation for the vertical displacement of any point on the string is y(x,t)= . (a)What are the frequency and wavelength of the fundamental mode of this string? (b)How long is the string? (c)How fast do waves travel on this string?

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.

Two violinists are trying to tune their instruments in an orchestra.One is producing the desired frequency of 440.0 Hz.The other is producing a frequency of 448.4 Hz.By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?

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?