Transverse Standing Waves?
A 37 cm length of wire has a mass of 6.0 g. It is stretched between two fixed supports and is under a tension of 160 N. What is the fundamental frequency of this wire?
- 1 decade agoFavorite Answer
fundamental is L=(1/2) x wavelength
L = 0.37 m so wavelength = 0.74
V= square root tension of the string divided by the mass per unit length of the string which is = 99.331
frequency = v/wavelength= 99.331/0.74=134.231 Hz
the fundamental frequency is 134.231 Hz
- Anonymous1 decade ago
Here's how to do it:
You are going to use the wave equation v=fλ but first you need to ascertain λ and v.
For a fixed wire, the fundamental mode has a node at each end and the longest wavelength that will satisfy this condition is λ=2L in other words you have 1/2 a wavelength on the wire.
So we get λ=2*0.37=0.74m.
Now the speed of the wave. The speed of the wave in a wire in v=√(T/μ) where 'T' is the tension in the wire and μ is the linear density (mass per unit length) of the wire.
So now you know λ and v you can simply substitute into the wave equation v=fλ to find the fundamental frequency.
- jbradshaw77Lv 41 decade ago
Is this your homework assignment?