Frequency, transverse waves, low-pitch strings

[rlc]

Homework Statement

Two identical guitar strings are stretched with the same tension between supports that are not the same distance apart. The fundamental frequency of the higher-pitched string is 380Hz, and the speed of transverse waves in both wires is 200 m/s. How much longer is the lower-pitched string if the beat frequency is 4Hz?

Homework Equations

None have worked!

The Attempt at a Solution

Every yahoo answers solution has not worked for me. Please help!

 

[BvU]

None meaning which ones ?

Have you attempted a solution ? If so, show your work. Every one of them that didn't work according to you. There must be a way out of this; perhaps one of the dead ends still has an opening somewhere ...

 

[rlc]

y=y0[sin(2pif1t)+sin(2pif2t)]

Is this the right equation to use?

 

[BvU]

you need something to connect tension, length and frequency. an equation where some or all appear.

If the beat frequency is 4 Hz, how much is the frequency of the lower-pitched string ?

 

[rlc]

f = (1/2L)*√(T/μ)
where

• f is the frequency in hertz (Hz) or cycles per second
• T is the string tension in gm-cm/s²
• L is the length of the string in centimeters (cm)
• μ is the linear density or mass per unit length of the string in gm/cm
• √(T/μ) is the square root of T divided by μ in seconds

The transverse wave speed v in a flexible string or wife is given by:
v=SQRT(T/u)
where T is tension and u is the mass per unit length of the string

Beats are the difference between two frequencies: ABSOLUTE VALUE OF (f1-f2)

 

[rlc]

I got it!
f=(1/2L)(transverse wave speed)
380=(1/2L)(200)
L=0.263157 m

Beat frequency=f1-f2
380-4=376 (I know that you can add or subtract the 4, but I went with subtracting first just to try)
376=(1/2L)(200)
L=0.265957

Subtract the two L's:
0.265957-0.263157=2.80E-3 m (which the online homework program says is the right answer)

 

[BvU]

It wasn't a matter of trial and error: they were specifically asking for the lower-pitched string.
Other than that: good work!
It shows how difficult playing string instruments really is: just a fraction away from the right position and you get undesired beats.