Standing Waves on a String (Melde's Experiment)

In summary, the conversation discusses a problem regarding standing waves in a string with 4 antinodes when a mass of 200 g is hanging over a pulley. The question is asking for the mass needed to produce a standing wave pattern with 6 antinodes. The equations for velocity, frequency, wavelength, tension, and mass are given, along with the diagram for reference. The solution involves finding the relative change in wavelength, which leads to determining the relative change in velocity, tension, and ultimately, the mass needed for 6 antinodes. The last equation is derived from the given equations and represents the relative change in mass.
  • #1
CHurst5841
1
0
The problem is as follows:

"A string exhibits standing waves with 4 antinodes when a mass of 200 g is hanging over the pulley (see attached figure). What mass will produce a standing wave pattern with 6 antinodes?"

The equations that I have found in the relevant section of the text are as follows:

[tex]v=\sqrt{\frac{T}{\mu}}[/tex]

[tex]v=f\lambda[/tex]

[tex]f=\frac{1}{\lambda}\sqrt{\frac{T}{\mu}}[/tex]

[tex]T=mg[/tex]

[tex]\frac{1}{n}=\frac{1}{Lf}\sqrt{\frac{T}{\mu}}=[\frac{1}{Lf}\sqrt{\frac{g}{\mu}}}]\sqrt{m}[/tex]

Where...
T = tension in the spring as supplied by the weight of the hanging mass
mu = linear density of the string
lambda = wavelength
f = frequency of oscillation
m = mass suspended from spring
g = gravitational constant
L = length of the string

I've attached the diagram referenced above for further illustration.

http://img180.imageshack.us/img180/3735/sc002c9a37ww1.th.jpg [Broken]

I have no idea where to even begin with the problem given the lack of information provided by the question.

Please help!
 
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  • #2
All the information you need is given. You need to find the relative change in the wavelength to determine the relative change in velocity, and from that determine the relative change in tension, and ultimately the relative change in the mass.
 
  • #3
therez no diagram attached to it ... can u please attach it again or give us a link for the diagram !
 
  • #4
Razi Rehman said:
therez no diagram attached to it ... can u please attach it again or give us a link for the diagram !


and can u explain how u got the last eqn after T=mg
 

What is a standing wave?

A standing wave is a type of wave that appears to be standing still, hence its name. It is created when two waves of the same frequency and amplitude traveling in opposite directions interfere with each other.

What is Melde's experiment?

Melde's experiment is a scientific experiment conducted by physicist Franz Melde in the 19th century to study the behavior of standing waves on a string. It involves setting up a string between two fixed points and using a device to produce vibrations, thus creating standing waves on the string.

How does Melde's experiment demonstrate standing waves?

In Melde's experiment, the string is fixed at both ends and a device, such as a tuning fork, is used to produce vibrations at a specific frequency. These vibrations travel along the string and reflect back and forth between the fixed points, creating a standing wave pattern that can be observed.

What factors affect the standing wave pattern in Melde's experiment?

The frequency and wavelength of the vibrations produced, as well as the tension and length of the string, can all affect the standing wave pattern in Melde's experiment. As these factors change, the number of nodes and antinodes in the standing wave will also change.

What are some real-life applications of standing waves on a string?

Standing waves on a string have many practical applications, such as in musical instruments like guitars and violins, where the strings vibrate to produce sound. They are also used in engineering to study structural vibrations and in medical imaging techniques like ultrasound.

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