Which harmonics would be observed on an electric guitar?

[thomas19981]

Homework Statement

The electric guitar radiates very little sound directly, but instead relies upon pick-ups (transducers) placed beneath the strings. Establish, showing clearly how you reach your answer, which harmonics of the open string you are likely to observe if the pick-ups are placed.
1)close to the bridge of the guitar.
2)around the mid-point of the strings
3)a quarter of the way from the bridge to the nut
4)$98 mm$ from the bridge, when the length of the open string is $648 mm$

Homework Equations

$n\lambda/2=L$

The Attempt at a Solution

I'm not totally sure what to do for all the above parts but I've derived the equation above to help me get the number of the harmonic I would observe. At a guess i'd say that the transducers give nodes so from that I can deduce n which would give me the number of the harmonic. Is that the right idea or am I totally wrong?
Thanks in advance

 

[BvU]

At a guess i'd say that the transducers give nodes

You may want to reconsider that (see here)

I'm not totally sure what to do

When in doubt, make sketches

 

[PeterO]

Homework Statement

The electric guitar radiates very little sound directly, but instead relies upon pick-ups (transducers) placed beneath the strings. Establish, showing clearly how you reach your answer, which harmonics of the open string you are likely to observe if the pick-ups are placed.
1)close to the bridge of the guitar.
2)around the mid-point of the strings
3)a quarter of the way from the bridge to the nut
4)$98 mm$ from the bridge, when the length of the open string is $648 mm$

Homework Equations

$n\lambda/2=L$

The Attempt at a Solution

I'm not totally sure what to do for all the above parts but I've derived the equation above to help me get the number of the harmonic I would observe. At a guess i'd say that the transducers give nodes so from that I can deduce n which would give me the number of the harmonic. Is that the right idea or am I totally wrong?
Thanks in advance

The pick-up works when the string just above it is moving.
Sketch the modes of vibration of a string, and check whether there will be a node (the string not moving) where the pick-up is.
Note: You said "At a guess i'd say that the transducers give nodes". On the contrary, the transducer will only detect/produce sound where there isn't a node.

 

[sophiecentaur]

After you have decided on the motion of the string, you should consider the fact that the signal produced by a guitar pickup is due to variable reluctance of the magnetic circuit containing the head and the steel string. This will introduce a large second harmonic component of the periodic motion of the string.