Where'd I go wrong (sound problems)

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The discussion revolves around calculating the linear mass density of a cord in a physics problem involving a mass and a standing wave. Initially, the wavelength was determined to be 2/3 m, leading to a wave velocity of 100 m/s. The tension in the rope was calculated as 49 N, but the user mistakenly treated mass as the desired variable instead of the linear mass density. Clarification was provided that the correct variable to solve for is the linear density, which is expressed as mass per unit length (kg/m). The user acknowledged the misunderstanding and expressed gratitude for the clarification.
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A mass of 5 kg hangs from a cord around a light pulley. The length between the vibrator and the pulley is 2 m. (A) When the vibrator is set to a frequency of 150 hz, a standing wave with 6 loops is formed. What must be the linear mass density of the cord?

First I figured the wave length was 2/3 m because there were 6 loops over 2 m

The Wavelength is equal to velocity over frequency

2/3 = V/150
V=100 M/s

V = the squareroot of Ft (force of tension in the rope) divided by the mass of length

The Squareroot of Ft/(m/L) = V
Ft = 49
L=2/3
m=desired variable
v=100

I got .0033 kg for the answer when I plugged this all in. The correct answer is .0049. Thanks for the help
 
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It looks good to me... Are you sure the "correct" answer is actually correct?
 
Jacob87411 said:
A mass of 5 kg hangs from a cord around a light pulley. The length between the vibrator and the pulley is 2 m. (A) When the vibrator is set to a frequency of 150 hz, a standing wave with 6 loops is formed. What must be the linear mass density of the cord?

First I figured the wave length was 2/3 m because there were 6 loops over 2 m

The Wavelength is equal to velocity over frequency

2/3 = V/150
V=100 M/s

V = the squareroot of Ft (force of tension in the rope) divided by the mass of length

The Squareroot of Ft/(m/L) = V
Ft = 49
L=2/3
m=desired variable
v=100

No, read the question again. m is NOT the desired variable, it is m/L that you are required to determine. You would have noticed this if you looked at the units of the solution, kg/m (not kg).

What you've done so far is correct, but now you just have to find the linear density, \rho = m/L from the equation :
\sqrt{{\frac{49}{\rho}}} = 100
 
Ahhh, thank you, that makes sense
 
Thread 'Variable mass system : water sprayed into a moving container'

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}...
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