Transverse wave through a wire, and tension.

AI Thread Summary
The discussion focuses on calculating the tension in a wire based on a transverse wave equation. The wave has a linear density of 2.35 g/m and is described by the equation y(x,t) = (1.4 cm)sin[(5.45 m⁻¹)x−(6950 s⁻¹)t]. Initial calculations for maximum velocity and wave speed were attempted, leading to an incorrect tension value. Clarification was provided that 6950 is indeed the angular frequency (omega), which helped resolve the confusion. Ultimately, the correct tension was calculated as approximately 22.25 N.
jmm5872
Messages
38
Reaction score
0
A transverse wave in a wire with a linear density 2.35 g/m has the form y(x,t) = (1.4 cm)sin[(5.45 m-1)x−(6950 s-1)t].
What is the tension?


I took the A=.014m, k=5.45 /m, and \omega=6950.

I used the formula for the max velocity = A\omega
v=(.014)(6950)=97.3

Then I used the formula for the speed of a wave on a string v=\sqrt{\frac{F}{M/L}}.
97.3=\sqrt{\frac{F}{.00235}}

And I got F=22.24813

This was not the correct answer. I would appreciate any advice.

I attempted to find the velocity of the pulse : (0.943s)(3.29m)(8)=24.81976
 
Physics news on Phys.org
Try using this equation for velocity:

v=\omega/k
 
Am I right in assuming that 6950 is omega? The problem says 6950 /s, not radians/s. Is this still omega?
 
Yes, that is still omega.
 
That worked, thank you very much.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top