Question

A violinist places her finger so that the vibrating section of a 1.00 g/m string has a length of 40.0 cm, then she draws her bow across it. A listener nearby in a 20 degrees Celcius room hears a note with a wavelength of 60.0 cm. What is the tension in the string?

Answer 1

first find the frequency heard...

speed of sound at 20 deg C = 343 m/s

   f = v / λ = 343 /0.60   = 571.7 Hz

Then... find the wavelength of the wave on the string:

   λ = 2L = 2 * 0.40 = 0.80 meters

Find the speed of the waves on the string:   speed = λ f = 0.80 * 571.7 =    457.3 m/s

Then use:     speed² = Tension / μ     or

   Tension = speed² *μ = 457.3² * 0.001 =    209.2 Newtons