Tension in an oscillating string

AI Thread Summary
The discussion centers on calculating the tension in a 120-cm-long string oscillating in its fourth mode at a frequency of 150 Hz. The initial attempt used the equation f = sqrt(TL/m)/2L but yielded an incorrect tension value of 324. It was clarified that the formula for wave velocity should be v = f * λ and v = sqrt(T/(m/L)), indicating a need to accurately determine wave speed. The participant realized that assuming a wave speed of 343 m/s was inappropriate without specific context about the medium. The conversation emphasizes the importance of using the correct wave speed for accurate tension calculations.
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Homework Statement


A 120-cm-long, 3.0 g string oscillates in its n = 4 mode with a frequency of 150 Hz and a maximum amplitude of 5.5 mm. Wavelength is 0.6 m.

What is the tension in the string?

Homework Equations


f = sqrt(TL/m)/2L


The Attempt at a Solution



150 = sqrt(1.2T/.003)/2.4

Solving for T gives me
T = 324
Which, according to the program(Mastering Physics), is wrong. I'm not sure if this is the right equation, but its the only found I could find that uses all of the information I have, excluding amplitude.
 
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The 2L only works if the string is at the fundamental harmonic. More generally, the velocity of a wave is v = f*l (in which f is frequency and l is wavelength) and v = Sqr(T/(m/L)), in which T is tension, m is mass, and L is string length.
 
Ah, thank you! I got it now. I was assuming 343 m/s for the velocity. Should I not assume, unless the problem explicitly says "through air"?
 

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