Linear density and tension problem

[HHH]

The string on the violin with the highest pitch is the note E, which has a frequency of 329.6 Hz and a wavelength of 1.032 m. If the string has a mass of 180.0 g and a length of 32.0 cm and is currently producing a wave of frequency 328.1 Hz, how much do you need to change the tension in the
string to produce the note E? Assume string length, string mass, and wavelength remain unchanged in the tuning process.

The back of the book says 1.35 N and i keep getting around 591 N

1. Solve for tension in string
v = 328.1*1.032
v = 338.5992 m/s

Linear Density (u) = 0.18/0.32
Linear Density (u) = 0.5625 kg/m

338.5992= sqrt(Ft/0.5625)
338.5992^2 = Ft/0.5625
114649.418*0.5625 = Ft
64490.297 = Ft

2. Solve for tension required for note E
v = 329.6 *1.032
v = 340.1472 m/s

Linear Density (u) = 0.18/0.32
Linear Density (u) = 0.5625 kg/m

340.1472= sqrt(Ft/0.5625)
340.1472^2 = Ft/0.5625
115700.117*0.5625 = Ft
65081.316= Ft

3. Find the difference in tension
Ft = 65081.316 - 64490.297
Ft = 591.019

 

[AAAA]

Your math seems fine, your textbook may be wrong. Unless I'm interpreting it incorrectly.

 

[ehild]

The string on the violin with the highest pitch is the note E, which has a frequency of 329.6 Hz and a wavelength of 1.032 m. If the string has a mass of 180.0 g and a length of 32.0 cm and is currently producing a wave of frequency 328.1 Hz, how much do you need to change the tension in the
string to produce the note E? Assume string length, string mass, and wavelength remain unchanged in the tuning process.

Something is very wrong with the data. The 180 g mass is impossible for a violin string! If it is a steel string, it would mean about 5 mm thick! An E string should have of 0.2-0.3 mm diameter!
That 180 g =0.18 kg should be rather 0.18 g.

Also note that the given wavelength of pitch E (1.32 m) refers to air. The wavelength in the chord is different and defined by the length of the chord.

 

[HHH]

Something is very wrong with the data. The 180 g mass is impossible for a violin string! If it is a steel string, it would mean about 5 mm thick! An E string should have of 0.2-0.3 mm diameter!
That 180 g =0.18 kg should be rather 0.18 g.

Also note that the given wavelength of pitch E (1.32 m) refers to air. The wavelength in the chord is different and defined by the length of the chord.

Is my process and math right? or no?

 

[ehild]

Is my process and math right? or no?

The wavelength is twice the chord length. The speed of the wave in the chord is that length multiplied by the frequency.