Where'd I go wrong (sound problems)

[Jacob87411]

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

 

[christinono]

It looks good to me... Are you sure the "correct" answer is actually correct?

 

[Gokul43201]

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 :
$$\sqrt{{\frac{49}{\rho}}} = 100$$

 

[Jacob87411]

Ahhh, thank you, that makes sense