Constituent traveling waves and strings and vibrations

[clairez93]

Homework Statement

A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:
A) 10 cm
B) 30 cm
C) 40 cm
D) 60 cm
E) 120 cm

Homework Equations

$$L = n(\frac{1}{4}\lambda)$$

The Attempt at a Solution

First, what I tried was this:
$$.30 = 2(\frac{1}{4}\lambda)$$
$$\lambda = .60$$

The answer, however, was C) 40 cm.

So, when I changed 2 to 3, like this:

$$.30 = 3(\frac{1}{4}\lambda)$$
$$\lambda = .40$$

I got the correct answer.

So, does the constituent traveling wave mean the wave with the next harmonic number? Somehow, I don't think that is correct. Constituent means 'component' and such.

I don't understand the concept behind this, why do you use the harmonic number of 3?

 

[Redbelly98]

It looks like by "harmonics", they mean only the allowed vibration modes and not simply multiples of the lowest-frequency mode.

You might try drawing a sketch of the "modes" or shapes of the string for n=1, 2, and 3. See if it makes sense that the n=2 case is not valid, given the condition of 1 fixed + 1 free end.

 

[clairez93]

Ah I see, since it's clamped at one end it can only have odd number harmonics correct? So the second harmonic they would mean n=3.