How Does Current Frequency Affect Wire Oscillation in a Magnetic Field?

[i_ammitija]

Homework Statement

A wire with an alternating current flowing through it is placed in a magnetic field. This causes the wire to oscillate with a frequency equal to the frequency of the current (you will learn about this when we study electromagnetism). The wire has a length (length is measured from the node at which the wire is tied to the pulley) L = 2.46 m. A mass of 244.0 g is hung on the end of the wire. The frequency of the current is initially set to f = 59.8 Hz. Three loops are observed in the wire at this frequency as shown in the diagram.

Image attached with this post!

Homework Equations

(2Lf)2= T/µ.

The Attempt at a Solution

µ = T/(2Lf)2 =(0.244*9.8)/(2* 2.46m*59.8 Hz)^2

This answer was wrong according when inserted!

Any help finding the velocity or the mass per unit length is kindly appreciated!

 

[mfb]

(2Lf)2= T/µ.

What does the second "2" mean?

Where did you calculate the wave-length of the oscillation (or, equivalently, where did you use the information that there are three loops)?

 

[i_ammitija]

What does the second "2" mean?

Where did you calculate the wave-length of the oscillation (or, equivalently, where did you use the information that there are three loops)?

I wasn't too sure how to incorporate that :/ I'm an economics student, doing this physics subject as an elective. I wasn't too sure how you could relate the three looops.

 

[mfb]

Imagine how the loop looks at some specific point in time. A bit like this: "^u^". How many wavelengths are this? And the next question, what is the wavelength then?

 

[Nickie]

I would first commend the student for attempting to apply the relevant equations and for seeking help when encountering difficulties. I would then offer the following response:

The equation you have used, (2Lf)^2 = T/µ, is the correct equation for determining the wave speed of a standing wave on a string, where L is the length of the string, f is the frequency of the wave, T is the tension in the string, and µ is the mass per unit length of the string. However, it is important to note that this equation assumes that the string is under tension and that the mass is evenly distributed along the length of the string.

In this problem, we are dealing with a wire that is not under tension, but is instead oscillating due to an alternating current in a magnetic field. In this case, the equation for the wave speed is different and is given by v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength of the standing wave. To determine the wavelength, you can use the fact that the number of loops in the standing wave is equal to the number of half-wavelengths in the wire. In this case, we can see that there are three loops, so the wavelength of the standing wave is equal to 2L/3. Using this value for λ, you can then calculate the wave speed v using the equation v = fλ.

Additionally, the mass per unit length of the wire is not given in the problem statement, so it cannot be calculated. It may be helpful to refer to your textbook or class notes for the appropriate value of µ for a wire of this type.

I hope this helps you to better understand the problem and to find the correct solution. Best of luck with your studies!