Solving Wave Speed of a Violin String

[HHH]

Homework Statement

A violin string with a mass of 0.35g is 33 cm long. The frequency of a wave supported by the string is 196 Hz.

What is the speed of the wave?

Homework Equations

Ln = n/2 *lambda
v = f*lambda

The Attempt at a Solution

1. Solve for wave length [/B]
L1 = 1/2 *lambda
0.33 = 1/2 * lambda
0.33 *2 = lambda
0.66 = lambda

2. Solve for speed of wave
v = f * lambda
v = 196 * 0.66
v = 129.36 m/s

I just assumed you have to use first harmonic and got the right answer, but why do we have to use first harmonic? or is there another way to do it?

 

[haruspex]

is there another way to do it?

You mean, without assuming 1st harmonic?
What if you assume 2nd harmonic? Does that give a different answer?

 

[HHH]

You mean, without assuming 1st harmonic?
What if you assume 2nd harmonic? Does that give a different answer?

1. Solve for wave length
L1 = 2/2 *lambda
0.33 = 2/2 * lambda
0.33 *1 = lambda
0.33 = lambda

2. Solve for speed of wave
v = f * lambda
v = 196 * 0.33
v = 64.68 m/s

I get that which is wrong

 

[haruspex]

1. Solve for wave length
L1 = 2/2 *lambda
0.33 = 2/2 * lambda
0.33 *1 = lambda
0.33 = lambda

2. Solve for speed of wave
v = f * lambda
v = 196 * 0.33
v = 64.68 m/s

I get that which is wrong

Quite so. So it follows that it is necessary to assume a particular harmonic, right?

 

[HHH]

Quite so. So it follows that it is necessary to assume a particular harmonic, right?

So is it just a poorly worded question. Or do you always use first harmonic if it doesn't say.

Also, In the question, it does however mention that the string supports 196Hz, so is that a minimum frequency→like a harmonic?

 

[haruspex]

it does however mention that the string supports 196Hz, so is that a minimum frequency→like a harmonic?

No, I think that just means it is one of the frequencies at which it can vibrate.
I note that it does give you the mass of the string, but that's no use without knowing the tension. Is there a later part to the question that asks you to find the tension?

 

[HHH]

No, I think that just means it is one of the frequencies at which it can vibrate.
I note that it does give you the mass of the string, but that's no use without knowing the tension. Is there a later part to the question that asks you to find the tension?

B) What is the linear density of the string?
C) What is the tension in the string?

Those are easy if you know the speed.