Question

Need help with physics!!

Answer 1

1. The frequency of vibration f of a string is related to the diameter d, length l, tension T and density D of the string according to the formula f= 1/dL sqrt T/D

a. What type of proportionality exists between f and T and why (what is constant, ratio or product)? Be specific ie direct square, direct cube, Inverse Square, etc.…
b. What type of proportionality exists between f and L and why? Be specific ie direct square, direct cube, Inverse Square, etc.…
c. Write a comparative equation for f vs L and T, while keeping d and D constant
d. What is the percent change in f if L were doubled and T were reduced by 35.0%

Answer 2

@Michele_Laino

Answer 3

@Anaise

Answer 4

@baru

Answer 5

@CandyCove

Answer 6

can you write that equation with the equation editor?

Answer 7

The standard equation which is normally used is \[f=\frac{1}{2L} \sqrt{\frac{T}{\mu}}\] where \[\mu\] is the mass per unit length.
The mass for a length L is \[\frac{\pi d^2}{4}LD\] so the mass per unit length is \[\frac{\pi d^2}{4}D\].
Putting this into the equation for the frequency gives \[f = \frac{1}{dL}\sqrt{\frac {T}{\pi D}}\] so I think that the equation stated @MTALHAHASSAN2 is missing a pi or was the pi missed out to make the question easier to deal with? It will make no difference to the answers.

Answer 8

I agree with Farcher; the formula should read: \(f=\dfrac{1}{dL}\sqrt {\dfrac{T}{\pi D}}\)
but the answers dealing with proportionality will remain the same.

Answer 9

For instance, if the relation is "y an inverse square of x", it means you can find an independent coefficient \(\alpha\) such as:
\(y=\alpha \times \dfrac{1}{x^2}\)