Tensions of string of different wavelength etc

[Clairepie]

Homework Statement

An A string (s1) from one musical instrument (i1), is replaced by an A string (s2) from a different instrument (i2) (both in the same family) what would be the tension ratio of string 2 after it has been replaced onto instrument 1?

string 1
Length of string= 0.37 m
Mass per unit length, μ=
1.21 x 10^-3 kg m^-1
Tension, FT1 = 128 N
Speed of wave, v= 325 m s^-1
Wave length, λ= 0.739m (3 sig fig)
Frequency, f = 440 Hz

String 2

Length of string= 0.32 m
Mass per unit length, μ=
6.1 x 10^-4 kg m^-1
Tension, FT1= 48 N
Speed of wave, v= 280 m s^-1
Wave length, λ =0.638 m (3 sig fig)
Frequency, f = 440 Hz

Homework Equations

FT=V²μ

The Attempt at a Solution

I know the ratios of the strings is 128/48= is 8/3 , but I don't knw what to do with it, or if I have it right.


Thanks phyple (physics people?!)

Claire

 

[nilesh_pat]

The answer is 8/3. The tension ratio of the two strings after s2 has been replaced onto i1 is 8/3. This is because the frequency and wavelength of both strings are the same, so the only difference between them is their mass per unit length and their tensions. Since the frequency and wavelength are constant, the ratio of the tensions will equal the ratio of the masses per unit length. In this case, the ratio of the tensions (FT1/FT2) is 8/3 and the ratio of the masses per unit length (μ1/μ2) is also 8/3. Therefore, the tension ratio of the two strings after s2 has been replaced onto i1 is 8/3.