Waves on a composite string
By When waves pass from one medium to other medium their speeds change. This phenomenon is called refraction in optics. A similar phenomenon occurs for waves passing on string. If the wave encounters a change is the density of the string its speed changes according to the mass per unit length of the string. In this experiment you will study a wave going on a combination of two strings tied to each other.
Procedure
You need a copper wire tied to a string, a function generator, vibrator, scale, a fixed support.
- Tie the end of the string to the vibrator and the end of the copper wire to the fixed support.
- Measure the length of copper wire and of the string. There will be considerable overlap of the two at the joint. Where would you take the junction? At the middle of the joint, at the string side of the joint or at the wire side of joint?
- Keep the tension in the string just sufficient to keep it nearly straight.
- Connect the function generator to the vibrator and switch it on. Keep the amplitude maximum. Gradually increase the frequency, starting from very low value.
- Adjust the frequency to get maximum vibrations in fundamental mode. There should be no node in between. Is the shape of the composite string symmetric about the mid point? What is the frequency at this stage?
- Now increase the frequency to get one node apart from the ends. Measure the distance of the node from the joint. Is it on the string or on the wire?
- Now adjust the frequency to get a node right at the junction. How many loops are there on the string? How many loops are there and on the wire?
- Measure the distance between consecutive nodes. What is the wavelength of the interfering waves on the string? What is the wavelength of the interfering waves on the wire?
- As the frequency is same for the string and the wire, \(v_1/\lambda_1=v_2/\lambda_2\).
Also tension has to be same on the two parts. Using \(v=\sqrt{T/\mu}\) calculate the value of \(r=\sqrt{\mu_w/\mu_{str}}\). Compare it with the known value of \(r_0=\sqrt{\mu_w/\mu_\text{str}}\) and calculate the percent difference from the actual value \(100(r-r_0)/r_0\).\end{enumerate}
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