Calculate the fundamental frequency of a steel rod

[timeforplanb]

Homework Statement

Calculate the fundamental frequency of a steel rod of length 2.00 m. What is the next possible standing wave frequency of this rod? Where should the rod be clamped to excite a standing wave of this frequency?

Homework Equations

F_n=nv/2L

The Attempt at a Solution

since the velocity of sound in steel was needed and it wasn't mentioned in the problem, i figured that i had to search for the value myself. i got the value of 6100 m/s.

for the fundamental frequency:
F₁=(v/2L)
F₁=((6100m/s)/(2x2m))
F₁=1525 Hz

for the next standing wave frequency:
for the fundamental frequency:
F₁=(2v/2L)
F₁=((2x6100m/s)/(2x2m))
F₁=3050 Hz

about the third problem though, i have no idea how to solve it.
the length of the rod could be determined by the equation L=λ/2 (λ=wavelength) when the clamp is at the center of the rod, right? what happens then if we move the clamp to another position? will there be a change in the wavelength or other parameters? more importantly, can anyone provide the equation needed to answer the third question? thank you very much.

 

[I like Serena]

Hi timeforplanb!

You might want try and visualize it.

Suppose we'd be talking about a string on a guitar.
If it's vibrating freely, both ends are fixed and the largest amplitude is in the middle.

This corresponds the the first half of a sinusoidal wave which is reflected on each end, resonating into a standing wave.

The next frequency up, would be a full wavelength in the string, meaning "still" in the middle, and with 2 maximum amplitudes at 1/4 and 3/4.

With a guitar, you can "force" the frequency by keeping your finger losely against the string at a place where you want a node.