Longitudinal waves in a clamped metal rod

[jemerlia]

Homework Statement

The speed of sound in a metal rod is 3600 m s -1. The rod is 1.20m
long and clamped at one of its ends.
(a) Determine the frequency of its vibration if longitudinal waves
are established in the rod and it is vibrating in its first overtone
mode.
(d) Determine the frequency of its vibration if clamped in the middle whilst still vibrating in the first overtone.

Homework Equations

v = f x w where w is the wavelength

The Attempt at a Solution

(a) The first overtone is the third harmonic, therefore
L = (3/4)w
= 3/4 x 1.60m
W = (4/3)L = (4/3) x 1.60m
f= 3600ms^-1 / (4/3 x 1.60m) = 1.69kHz; given answer is 2250 Hz

(d) Still the third harmonic but L is now 0.8m
f = 3600ms^-1 / (4/3 x 0.80m) = 3.38kHz; given answer is 4500 Hz

What have I done wrong?

 

[Redbelly98]

The rod length is 1.20 m, not 1.60 m.