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PHYWE Phase Velocity of Rope Waves |
Learn about:
- Wavelength
- Phase velocity
- Group velocity
- Wave equation
- Harmonic wave
A rope is attached to an electromagnetic vibrator at one end with the other end going over a pulley and attaching to a pan of weights. The frequency of vibration is adjusted so that a stationary wave is produced in the rope for a fixed tension. The wavelength of the wave produced is calculated. Phase velocity (c) of the rope wave is calculated by multiplying the wavelength (?) of the stationary wave produced with the frequency of vibration (v), recorded by the wave generator, i.e., c= ? v. Assuming that the wave velocity (c) depends only on tension (T) and mass per unit length (΅) of the string, we can use dimensional analysis to find how 'c' depends on these quantities. So the result is; phase velocity, c, is proportional to (T/ ΅)1/2. The proportionality constant cannot be fixed by the dimensional analysis. The value of the constant can be obtained from a mechanical analysis of the problem or from experimental results. These methods show that the constant is equal to unity and the final result is: c=(T/ ΅)1/2. By measuring T and ΅ we can again calculate c which should match the result by measurement of d? and v.
In this experiment a quadrangular rubber rope is inserted through the demonstration motor and a linear polarized fixed wave is generated. With the help of a stroboscope, the frequency and the wave length are determined. Then the phase velocity of rope waves with a fixed tensile stress is ascertained. Subsequently, the mathematical relationship between the phase velocity of the rope and the tensile on the rope is examined.
Use this experimental setup to:
1. Determine the phase velocity c of the waves produced. For constant tensile stress, the frequency v depends on the wavelength ? of the wave that propagates itself along the rope. By plotting the frequency dv as a function of 1/?, one may obtain a linear relationship whose slope is the phase velocity c.
2. Compare the phase velocity c obtained in 1 to the value of c obtained from the measured tensile stress and the mass per unit length of the rope.
Includes a digital stroboscope; 2m measuring tape; 200m silk thread; PASS support system; 10 N spring balance; fixed pulley on 65 mm dia. Rod; 10 m cotton cord; 10/1 gearing,; 220 VAC motor; 10 m rubber strip and Hoffmann grooved wheel; and instructions.
For your convenience this experiment is available to you as a complete set.
Everything you require to perform the activities are included in the total price.
For assistance in using your new equipment we also offer professional development (WLS1808-24) on all PHYWE line products.
For customization options and pricing please contact your local Cenco representative.
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