Solving the Sound Wave Problem of Two Identical Violin Strings

[Lakers08]

Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously.

-What is the highest possible fundamental frequency of the retuned string?
-What is the lowest possible fundamental frequency of the retuned string?
-By what fractional amount was the string tension changed if it was increased?
-By what fractional amount was the string tension changed if it was decreased?

please help me get started I am totally stomped, thanks

 

[Tide]

HINT: The beat frequency is the difference between the two frequencies.

 

[Lakers08]

thanks a lot, lol for some reason i had the equation with a plus sign, thanks for the hint if it wasent for you i would be stuck here all night.

 

[Lakers08]

ummm just ran into another problem in this question, for the third part "by what fractional amount was the string changed?"

Iam using that the fundamental frequency of a string is proporional to the velocity of the waves which is proportional to the square root of the Tension in the string:

for example : f_2 = sqrt(T2/T1)*f_1

I am plugging in the frequency that i got for part a? for example 440 will go on f_1 and 442 will go on f_2 and then i solve for the ratio of T2/T1 but somehow I am missing something or I am doing this wrong, someone please help

 

[Tide]

HINT:

$$\frac {\delta T}{T} = 2 \frac {\delta f}{f}$$

 

[Lakers08]

thanks a lot