Speed of a wave on a string

[sheri1987]

Homework Statement

The mass of a string is 9.00 10-3 kg, and it is stretched so the tension in it is 120 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?

Homework Equations

1)velocity = frequency*wavelength
2)velocity = sqroot(F/(m/L))

The Attempt at a Solution

I thought i needed to calculate the velocity first, so I used the frequency of 260 * wavelength of .6 and got 156 m/s...then I plugged that in for v into the second equation and also 9.00E-3 as the mass and F is equal to the 120 ...what am I doing wrong, I tried solving for L?

 

[mda]

Looks like you are correct so far... why do think you are wrong?
Just solve for L, being careful to treat the velocity correctly...

 

[Moetasim]

I would first like to commend you for attempting to solve this problem on your own. Your approach is correct, but there might be some calculation errors in your solution.

To find the length of the string, we need to use the equation v = √(F/(m/L)), where v is the velocity, F is the tension, m is the mass of the string, and L is the length of the string. We can rearrange this equation to solve for L, which gives us L = (F/m)*(1/v^2).

Plugging in the values given in the problem, we get L = (120 N)/(9.00E-3 kg)*(1/(156 m/s)^2) = 0.054 m.

Therefore, the length of the string is 0.054 m. It is always important to double-check your calculations and make sure you are using the correct units. In this case, the units for velocity should be m/s, so make sure to convert 156 m/s to the correct units before plugging it into the equation.

 

[ogb p]

I can confirm that your approach to solving this problem is correct. The equation you used, velocity = frequency*wavelength, is the correct formula for calculating the velocity of a wave on a string.

Your calculation of 156 m/s for the velocity is also correct. However, when you plug that value into the second equation, you made a mistake in your units. The units for the tension, F, are in Newtons (N), and the units for the mass, m, are in kilograms (kg). Therefore, when you plug in 156 m/s for velocity, you need to convert the tension from 120 N to kg by dividing by the acceleration due to gravity (9.8 m/s^2):

120 N / 9.8 m/s^2 = 12.24 kg

Now, when you plug in the values for velocity and mass into the equation, you should get a value for the length of the string:

156 m/s = sqroot(12.24 kg/(L))

Solving for L, we get:

L = (12.24 kg)/(156 m/s)^2 = 0.0049 m

Therefore, the length of the string is 0.0049 m or 4.9 mm. It is important to always check your units and make sure they are consistent throughout your calculations. I hope this helps!