# Finding Mass for a Standing Wave in a Horizontal String

• MK7_Ironman
In summary, the conversation is about finding the mass needed to produce a standing wave with a given number of loops on a horizontal string attached to a mechanical vibrator. The linear density of the string is given, and the equations involving wave velocity, wavelength, and frequency can be used to solve the problem. The user is asking for help in finding the appropriate equations to use.
MK7_Ironman

## Homework Statement

One end of a horizontal string of linear density 4.7 multiplied by 10-4 kg/m is attached to a small-amplitude mechanical 58 Hz vibrator. The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11-48. Assume the string at the vibrator is a node, which is nearly true.

What mass must be hung from this end of the string to produce a standing wave with the following number of loops?

a). one loop: ?
b). two loops: ?
c). five loops: ?

## Homework Equations

I don't know how to do this problem that is why I'm asking.

## The Attempt at a Solution

I really don't know where to start that is why I need help please!

Welcome to PF

You'll have to come up with something before receiving help here. How about finding what equations have something to do with wave velocity, wavelength, and frequency?

Also, they gave you the linear density of the string in the problem statement. There's probably an equation that uses that, which will be useful here.

## 1. How do you find the mass for a standing wave in a horizontal string?

To find the mass for a standing wave in a horizontal string, you will need to know the frequency of the wave, the tension in the string, and the wavelength of the wave. You can then use the formula: mass = (tension * wavelength) / (2 * frequency^2). This formula is derived from the equation of motion for a standing wave on a string.

## 2. What is a standing wave?

A standing wave is a wave that oscillates in a fixed position rather than travelling through space. It is formed when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other to create a pattern of nodes and antinodes. Standing waves are commonly seen in musical instruments and other mechanical systems.

## 3. Why is it important to find the mass for a standing wave in a horizontal string?

Finding the mass for a standing wave in a horizontal string is important for understanding the dynamics of the wave and its behavior. It can also help in designing and calibrating instruments that use standing waves, such as musical instruments or sensors. Additionally, knowing the mass can provide valuable information about the properties of the string itself.

## 4. What factors affect the mass of a standing wave in a horizontal string?

The mass of a standing wave in a horizontal string is primarily affected by the tension in the string, the frequency of the wave, and the wavelength of the wave. As any of these factors change, the mass of the standing wave will also change. Other factors that may have a smaller impact include the density and diameter of the string.

## 5. Can the mass of a standing wave in a horizontal string be measured experimentally?

Yes, the mass of a standing wave in a horizontal string can be measured experimentally by using the formula mentioned in the first question. You will need to measure the frequency of the wave, the tension in the string, and the wavelength of the wave, which can be done using various experimental techniques. However, it is important to note that this measurement may have some errors due to the limitations of measurement instruments and the assumptions made in the formula.

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