How to produce a standing wave question

[michaelraymen]

Homework Statement

using a wire of length L= 1 M with both ends fixed, can you produce a standing wave with the following wavelengths? Explain why or why no.

a. 30 cm:

b. 1m :

c. 75 cm :

d. 2 m :

Homework Equations

L=n. (λn/2)

The Attempt at a Solution

1m= n. 30 cm/2 ?

 

[HallsofIvy]

A standing wave must fit a full "wave" inside the given length. In other words the length must be an integer multiple of the wavelength.

 

[michaelraymen]

So would all of the wave lengths work except for the 2 meter one?And How can I explain it with the formula?

Thank you for your help.

 

[berkeman]

Homework Statement

using a wire of length L= 1 M with both ends fixed, can you produce a standing wave with the following wavelengths? Explain why or why no.

a. 30 cm:

b. 1m :

c. 75 cm :

d. 2 m :

Homework Equations

L=n. (λn/2)

The Attempt at a Solution

1m= n. 30 cm/2 ?

A standing wave must fit a full "wave" inside the given length. In other words the length must be an integer multiple of the wavelength.

For a string or wire fixed at both ends, the fundamental mode fits a half wavelength between the nodes, no?

 

[berkeman]

So would all of the wave lengths work except for the 2 meter one?And How can I explain it with the formula?

Thank you for your help.

Welcome to the PF.

I'd suggesting sketching each of the possible answers, to see if you get a whole number of half wavelengths between the nodes.