Hooke's law and wave velocity related problem

[harini07]

Homework Statement

The extension in a string, obeying hooke’s law is Y when wave velocity in it is V. if extension is increased to 1.5Y, then wave velocity V’ becomes?

1) V' =V. 2)V'= 1.22V . 3)V'=1.5V. 4) V'=0.75V.

Homework Equations

wave velocity= frequency*wave length.

The Attempt at a Solution

the frequency will be unchanged in both the cases, so v/v' = Y/1.5Y , which gives V'= 1.5V. but this is not the answer. where did i go wrong?

 

[DrClaude]

The extension in a string, obeying hooke’s law is Y when wave velocity in it is V.

Do you mean tension?

 

[harini07]

Do you mean tension?

nope. it's the extension and not tension.

 

[DrClaude]

So your are simply changing the length of the string.

the frequency will be unchanged in both the cases

Have you ever played a guitar (or seen someone playing one)?

 

[harini07]

So your are simply changing the length of the string.

Have you ever played a guitar (or seen someone playing one)?

except in movies no.

 

[DrClaude]

Think about how someone changes the notes on a guitar.

By the way, it would be helpful if you came up with more "relevant equations."

 

[harini07]

Think about how someone changes the notes on a guitar.

By the way, it would be helpful if you came up with more "relevant equations."

in particularly? there is this hooke's law which states F(force) = -K(spring constant)*x (extension). how to relate this with wave velocity?

 

[DrClaude]

You have to consider equations that include wave velocity. See http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html#c2

 

[harini07]

You have to consider equations that include wave velocity. See http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html#c2

so on using that equation i get something like this, V/V' = (y/1.5y)^1/2. when i substitute T=FL/Ay in that equation. is that right?

 

[DrClaude]

I realize now that the problem statement is not clear. How is the extension changed? By taking a longer length of the same string, or stretching it? I was assuming the former.

 

[Chestermiller]

Do you know the equation for the wave velocity of a string as a function of the string tension? The equation has to take into account the fact that the string has mass.

 

[harini07]

Do you know the equation for the wave velocity of a string as a function of the string tension? The equation has to take into account the fact that the string has mass.

Yup. V=√(T/mass per unit length). Substituting T for Y*area*extension/original length. Since the other components like mass, length,Young's modulus,area are unchanged, I'm equating V/V' =√(y/1.5y). Which gives V/V' = 0.82. thus I'm getting V' = 1.21V. Is this method correct?

 

[Chestermiller]

Yup. V=√(T/mass per unit length). Substituting T for Y*area*extension/original length. Since the other components like mass, length,Young's modulus,area are unchanged, I'm equating V/V' =√(y/1.5y). Which gives V/V' = 0.82. thus I'm getting V' = 1.21V. Is this method correct?

Yes.