Mariah Sparks

2022-07-21

An aluminum rod 1.60 m long is held at its center. It is strOked with a rosin-coated cloth to set up a longitudinal vibration. The speed of sound ina thin rod of aluminum is 5100 m/s. (a) What is the fundamental frequency of the waves established in the rod? (b) What harmonics are set up in the rod held in this manner? (c) What would be the fundamental frequency if the rod were copper, in which the speed of sound is 3560 m/s?

losnonamern

We are given following data for an aluminum rod held at its center:
L=1.6m
${v}_{al}=5100\frac{m}{s}$
A) Calculating the fundamental frequency:
$f=\frac{{v}_{al}}{2\ast L}=\frac{5100}{2\ast 1.6}=1594Hz$
B) Odd harmonics only are set up in the rod because the rod is fixed at its center.
C) Calculating the fundamental frequency if rod is made of copper, ${v}_{c}=3560\frac{m}{s}:$
$f=\frac{{v}_{c}}{2\ast L}=\frac{3650}{2\ast 1.6}=1113Hz$
Result:
A) f=1594Hz
B) Odd harmonics only are set up in the rod becaUse the rod is fixed at its center.
C)f=1113Hz

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