In the figure below, a string tied over a support at  Q, is stretched by a block of mass m.  Separation L = 1.20 m, linear density μ = 1.6 g/m, ant the oscillator frequency f = 120.0 Hz.  Assume P and Q are nodes.  What mass m allows the oscillator to set up the fourth harmonic on the string?  Determine the wavelength based upon the length and the number of waves shown in the figure.  Then, determine the required tension required to achieve the necessary velocity v=λf and v=(T/μ)0.5.  Then determine the mass necessary to achieve this tension.  T = mg.  Use g = 10 N/kg

400 kg machine is placed at the mid span of a 3.2 m simply supported steel beam (E=200\times10^9~N/m2) The machine is observed to vibrate with a natural frequency of 9.3 Hz. What is the size of the beam's cross section if the height is twice as the width, considering that:

Does an automobile radio antenna vibrate in resonance dueto vortex shedding? Consider an antenna of length L anddiameter D . According to beam vibration theory [, the fi rst mode natural frequency of a solidcircular cantilever beam is ω n = 3.516[ EI /( ρ AL 4 )] 1/2 ,where E is the modulus of elasticity, I is the area momentof inertia, ρ is the beam material density, and A is the beamcross-section area. ( a ) Show that ω n is proportional to theantenna radius R . ( b ) If the antenna is steel, with L = 60 cmand D =4 mm, estimate the natural vibration frequency, inHz. ( c ) Compare with the shedding frequency if the carmoves at 65 mi/h.

One of the strings of a bass viol is 0.640 m long and has a fundamental frequency of 165 Hz. What is the speed of waves on this string? When this string vibrates at its fundamental frequency, it causes the air in a nearby stopped organ pipe to vibrate at that pipe's fundamental frequency. The speed of sound in the pipe is 344 m/s. What is the length of this pipe?