A 50-cm long wire with a mass of 1 g and a tension of 440N passes across the ope

Question

A 50-cm long wire with a mass of 1 g and a tension of 440N passes across the open top of a vertical tube partially filled with water. The wire, which is fixed at both ends, is plucked at the center and set to vibrate at its fundamental frequency. This vibration, in turn, generates a sound wave. When the water level in the tube is slowly lowered, eventually a standing wave is generated in the tube. As the water level is then lowered by another 36cm. the next standing wave is detected. Use this information to work out the speed of sound in air at room temperature.

Explanation / Answer

We can go through the derivation
using Newton's law and the wave
equation, but I think we're talking
about matching the natural frequencies
of both physical objects. In this case
the fundamentals:

The string:
f1s = (1/2*L) Sqrt(T/u))

f1t = v / 4*L_t

m = 0.001 kg
T = 440 N
L = 0.5 m
u = m / L

u = 0.002

v = 0.36 m

f1s = (1 / 2 * L)) * Sqr(T / u)

f1s = 117.26

f1t = v / 4*L

117.26 = v / (4*0.5)

v = 234.52

f1t =

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