1. Suppose that a string has a length L. What is the largest possible wavelength

Question

1. Suppose that a string has a length L. What is the largest possible wavelength of a standing wave that can be supported by this string? Show your work.

2. What are the conditions (with respsect to the points of zero amplitude and maximum amplitude) that must hold to produce a standing wave on a vibrating string?

3. How is the length of the string L related to the wavelength for standing waves?

4. A student measure the tension in a string Ts=50N. If the mass per unit length of the string is p=14 grams/m, what is the speed of the wave on the string?

Explanation / Answer

1.
Ends of the string are attached to a fixed point. which are unable to move. So, for a standing wave, the ends become node and the anti nodes lies between the nodes.
The condition for standing wave is
n/2 = L
For maximum wavelength, n = 1
= 2L (There is only one anti node)

2.
The conditions are
The wavelength of the standing wave must fit with the length of the string.
At the two ends of the string, there will be only nodes.

3.
n = 2L
n = 1, 2, 3...

4.
Ts = 50 N
P = 14 g/m = 0.014 kg/m
velocity = sqrt[Ts/p]
= sqrt[50 / 0.014]
= 59.76 m/s.

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