# Hooke's law and wave velocity related problem

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1. Jan 30, 2017

### harini07

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
wave velocity= frequency*wave length.

3. 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?

2. Jan 30, 2017

### Staff: Mentor

Do you mean tension?

3. Jan 30, 2017

### harini07

nope. it's the extension and not tension.

4. Jan 30, 2017

### Staff: Mentor

So your are simply changing the length of the string.
Have you ever played a guitar (or seen someone playing one)?

5. Jan 30, 2017

### harini07

except in movies no.

6. Jan 30, 2017

### Staff: Mentor

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."

7. Jan 30, 2017

### harini07

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

8. Jan 30, 2017

### Staff: Mentor

9. Jan 30, 2017

### harini07

10. Jan 30, 2017

### Staff: Mentor

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.

11. Jan 30, 2017

### Staff: Mentor

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.

12. Feb 1, 2017

### harini07

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?

13. Feb 1, 2017

Yes.