The fundamental frequency of vibration of a particular string is f. What would the fundamental frequency be if the length of the string were to be halved and the tension in it was to be increased by a factor of 4?

Question

anonymous · Answer

Frequency is proportional to sqrt(tension) and inv proportional to length...

anonymous · Answer

The frequency is inversely proportional to the wavelength - and proportional to the square root of the tension.  So if my mental math is right, the answer is 4f.

anonymous · Answer

it is right cause i have the answer, but can you draw, the working exactly pls :)

anonymous · Answer

$$f = c/\lambda = \sqrt(T/\mu) / \lambda$$
Now go into this equation and replace T with 4T and lambda with lambda/2.  You should find that this has the overall effect of multiplying the right hand side by 4.