Solving String Tension: Wavelength, Speed and Frequency

AI Thread Summary
The discussion focuses on calculating the speed of a string under tension and its frequency based on different wavelengths. The speed of the string is calculated using the formula v = sqrt(Tension/(m/L)), yielding 283 m/s for a 1m wavelength and 200 m/s for a 0.5m wavelength. The frequency is derived from the relationship f = v/wavelength, resulting in 400 Hz for the 0.5m wavelength scenario. There is confusion regarding the application of linear mass density and whether it should remain constant across different wavelengths. The thread emphasizes the importance of understanding how tension and mass density affect wave speed and frequency in strings.
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Homework Statement


string is under tension 400N. A 1m string has mass 5grams. what is the speed if the wavelength is 1m. What is the speed if the wavelength is .5m. What is the frequency?


Homework Equations


v = sqrt(Tension/(m/L))
v = f * wavelength


The Attempt at a Solution



a) v = sqrt(400N / (.005kg/1m) = 283m/s

b) I am confused. whether to use the first or second equation?
v=sqrt(400N/.005kg/.5m) = 200m/s

c) f = v/wl = 200m/.5ms = 400Hz

is this correct?
 
Last edited:
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just a push in the right direction would be highly appreciated
 
L is the entire length of the string. Why would the linear mass density, something that is inherent and doesn't change with the same string, be changing?
 
so for b) would it be 1m for both, or is the speed impossible to derive from that formula?
 
If V=\sqrt{\frac{T}{\mu}}

What do you hypothesise if mu and T are always constant?
 

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