How Do You Calculate Wave Properties and Tension in a String?

[tymartin]

A string has a mass of 0.02 kg that's 25 m long. The wave has a frequency of 3 Hz. Find the amplitude, wavelength, and velocity of the wave and tension in the rope. Would really appreciate any help on this question. Having a terrible time with it.

 

[Astronuc]

Perhaps one's text has a discussion regaring frequency f, tension T, and mass per unit length m/L.

Otherwise, please refer to http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html#c2

There is also a relationship between the wave speed and the aforementioned variables.

 

[nlightner]

I would be happy to assist you with this question. To find the amplitude, wavelength, and velocity of the wave, we can use the equation v = fλ, where v is the velocity, f is the frequency, and λ is the wavelength. First, we can calculate the velocity by multiplying the frequency (3 Hz) by the wavelength (25 m). This gives us a velocity of 75 m/s.

Next, to find the wavelength, we can rearrange the equation to λ = v/f. Plugging in the values we already know, we get a wavelength of 25 m. This tells us that the wave is a standing wave, with one full wavelength fitting on the string.

To find the amplitude, we can use the equation A = y_max - y_min, where A is the amplitude, y_max is the maximum displacement of the wave, and y_min is the minimum displacement of the wave. Since we know that the wave is a standing wave, the maximum displacement will be twice the amplitude, and the minimum displacement will be zero. Therefore, the amplitude is 12.5 m.

To calculate the tension in the rope, we can use the equation T = μv^2, where T is the tension, μ is the mass per unit length (in this case, 0.02 kg/25 m = 0.0008 kg/m), and v is the velocity. Plugging in the values, we get a tension of 4.5 N.

I hope this helps you with your question. If you have any further questions, please don't hesitate to ask. I am always happy to assist with any scientific inquiries.