A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes?
The stretch in the wire is 18cm
The stretch in wire, ∆x= 8 cm =0.08 m The three antinodes are produced, n=3
Let the wavelength is denoted by λThe wavelength of the nth harmonic frequency is given by
Here n=3,Let the tension in the string is denoted by TThe expression of tension is given by T= k∆xHere, k is the spring constant for wire.
Now, the fundamental frequency of the wave is given by
Substitute the values Now, to get two antinodes, n=2, wavelength λ2 isThe stretch in the wire for this case is ∆x’
Now the frequency of the wave in this case is
Compare both the equations ∆x’= 18 cm
Thus the stretch in the wire is 18cm
A soap bubble is essentially a very thin film of water 1n = 1.332 surrounded by air. The colors that you see in soap bubbles are produced by interference.
a. Derive an expression for the wavelengths lC for which constructive interference causes a strong reflection from a soap bubble of thickness d. Hint: Think about the reflection phase shifts at both boundaries.
b. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?
As the captain of the scientific team sent to Planet Physics, one
of your tasks is to measure g. You have a long, thin wire labeled
1.00 g/m and a 1.25 kg weight. You have your accurate space cadet
chronometer but, unfortunately, you seem to have forgotten a
meter stick. Undeterred, you first find the midpoint of the wire by
folding it in half. You then attach one end of the wire to the wall
of your laboratory, stretch it horizontally to pass over a pulley at
the midpoint of the wire, then tie the 1.25 kg weight to the end
hanging over the pulley. By vibrating the wire, and measuring
time with your chronometer, you find that the wire’s second harmonic
frequency is 100 Hz. Next, with the 1.25 kg weight still
tied to one end of the wire, you attach the other end to the ceiling
to make a pendulum. You find that the pendulum requires 314 s to
complete 100 oscillations. Pulling out your trusty calculator, you
get to work. What value of g will you report back to headquarters?
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