Find the Minimum Length of a Vibrating String

[vijayramakrishnan]

Homework Statement

the equation of a stationary wave produced on a string whose both ends are fixed is given by
y= [0.6sin(pi/10)x]cos(600pi)t
what could be the smallest length of string?

Homework Equations

k=2pi/wavelength

The Attempt at a Solution

i got the wavelength to be 20 but don't know how to proceed,in the solution it is given that
"since the string is fixed at both ends the minimum length should be half of the wavelength"i couldn't understand this statement why should it be half?please explain

 

[Suraj M]

Okay Vijay
But what exactly are you supposed to find?

 

[vijayramakrishnan]

Okay Vijay
But what exactly are you supposed to find?

sir we are supposed to find the minimum length of the string.it has been given in the question sir.

 

[Suraj M]

As the string is attached on both sides, it's should contain 2 nodes on each end is what I think, so in which case would there be the least number (or fraction ) of both nodes and internodes
Try drawing all the cases you can think of.
I hope I'm helpful

 

[vijayramakrishnan]

As the string is attached on both sides, it's should contain 2 nodes on each end is what I think, so in which case would there be the least number (or fraction ) of both nodes and internodes
Try drawing all the case you can think of.
I hope I'm helpful

thank you,since the two ends must be at rest so they must be nodes and by finding the distance between two consecutive nodes we get the answer.i think this the explanation

 

[Suraj M]

So, the answer?

 

[gneill]

i got the wavelength to be 20 but don't know how to proceed,in the solution it is given that
"since the string is fixed at both ends the minimum length should be half of the wavelength"i couldn't understand this statement why should it be half?please explain

You should be able to do a bit of research to find an explanation. Did you try a web search on "string vibration modes"? Do so and take a look at the Hyperphysics web page (Standing Waves on a String) that turns up in the search results.

 

[vijayramakrishnan]

So, the answer?

it is half of wavelength that is 10.