Wavelength and Fundamental Frequency of Standing Wave on 2m String

[pooka]

A standing wave resonates at 400 Hz with three antinodes on a string tied tightly between two posts 2.0 meters apart.
What is the wavelength of this standing wave?
What is the fundamental frequency of this string?

I tried to draw the picture out, and it looks like the wavelength is just 2.0 m? I am not sure how to find the fundamental frequency though.

 

[alphysicist]

Hi pooka,

A standing wave resonates at 400 Hz with three antinodes on a string tied tightly between two posts 2.0 meters apart.
What is the wavelength of this standing wave?
What is the fundamental frequency of this string?

I tried to draw the picture out, and it looks like the wavelength is just 2.0 m?

Before dealing with the fundamental frequency, I don't believe this wavelength is correct. If you look at it again, do you see what it is? Or if not, why did you choose 2m as the wavelength?

 

[pooka]

Hi pooka,



Before dealing with the fundamental frequency, I don't believe this wavelength is correct. If you look at it again, do you see what it is? Or if not, why did you choose 2m as the wavelength?

I chose this wavelength because when I drew the wave out, the post is 2 metres apart, so I thought that the wavelength would also be 2 metres.

 

[pooka]

Okay I just redrew the wave. Is the wavelength 4/3 metres then?

 

[alphysicist]

Okay I just redrew the wave. Is the wavelength 4/3 metres then?

That sounds right to me.

For your question in your original post, what is the definition of the fundamental frequency? Try drawing this string vibrating in its fundamental frequency (instead of the frequency they give you). Can you find its wavelength in that case? Does that help you find its frequency?

 

[pooka]

That sounds right to me.

For your question in your original post, what is the definition of the fundamental frequency? Try drawing this string vibrating in its fundamental frequency (instead of the frequency they give you). Can you find its wavelength in that case? Does that help you find its frequency?

Is the fundamental frequency wavelength 4 m then?

 

[alphysicist]

Is the fundamental frequency wavelength 4 m then?

Yes, that is the wavelength when it vibrates at its fundamental frequency.

 

[pooka]

thanks!

 

[alphysicist]

Sure, glad to help! (Just to be sure I understood the wording in one of your posts, you did use that 4m wavelength to find the fundamental frequency, right?)

 

[pooka]

Sure, glad to help! (Just to be sure I understood the wording in one of your posts, you did use that 4m wavelength to find the fundamental frequency, right?)

Yup! The fundamental frequency is given by fn = v/λn.
I first found v by using the v = fλ where f is the 400 Hz times the wavelength 4/3

Then I divided the v by 4.