# 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?

Relevance

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

• Anonymous

Hi

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.

T=160N

μ=0.006/0.37=0.0162 kg/m

v=√(T/μ)=v=√(160/0.0162)=99.4m/s

So now you know λ and v you can simply substitute into the wave equation v=fλ to find the fundamental frequency.

v=fλ

f=v/λ

f=99.4/0.74=134Hz