Frequency and Length: Solving for String Length

[goonking]

Homework Statement

Homework Equations

The Attempt at a Solution

for the first harmonic, the wavelength is twice the length of string.
so 0.296m x 2 = 0.592m is the wavelength

with the wavelength and frequency known, we solve for v in v = ƒλ

v = 0.592m x 440 Hz = 260 m/s

then to solve for the length of new string , we just use the same v (260 m/s) and use the new frequency (523 Hz) and solve for the L?

if so , I got 24.9 cm

 

[haruspex]

Homework Statement

View attachment 89239

Homework Equations

The Attempt at a Solution

for the first harmonic, the wavelength is twice the length of string.
so 0.296m x 2 = 0.592m is the wavelength

with the wavelength and frequency known, we solve for v in v = ƒλ

v = 0.592m x 440 Hz = 260 m/s

then to solve for the length of new string , we just use the same v (260 m/s) and use the new frequency (523 Hz) and solve for the L?

if so , I got 24.9 cm

With regard to the parts of the string, what length have you calculated as 24.9cm? What length does it ask for?

 

[goonking]

With regard to the parts of the string, what length have you calculated as 24.9cm? What length does it ask for?

i calculated the length starting from beneath the finger to the nut to be 24.9 cm

 

[haruspex]

i calculated the length starting from beneath the finger to the nut to be 24.9 cm

What part of the string is vibrating at 523Hz?

 

[goonking]

What part of the string is vibrating at 523Hz?

just the 24.9 cm of string between the finger and nut I suppose since the rest isn't vibrating

 

[haruspex]

just the 24.9 cm of string between the finger and nut I suppose since the rest isn't vibrating

What is being used to make the string vibrate? What part of the string is it acting on?

 

[goonking]

What is being used to make the string vibrate? What part of the string is it acting on?

to make the string vibrate, you would have to pluck it, and if you held the string down with your thumb, only the part of the string between your thumb and the nut, will vibrate.

 

[haruspex]

to make the string vibrate, you would have to pluck it, and if you held the string down with your thumb, only the part of the string between your thumb and the nut, will vibrate.

You could do that, but you would get hardly any sound out of the violin. Whether played with a bow (as in the diagram) or plucked, it is the part between the bridge and the finger that is plucked or bowed. (The vibration is transferred through the bridge to the broad wooden lamina, and thence to the air inside.)

 

[goonking]

You could do that, but you would get hardly any sound out of the violin. Whether played with a bow (as in the diagram) or plucked, it is the part between the bridge and the finger that is plucked or bowed. (The vibration is transferred through the bridge to the broad wooden lamina, and thence to the air inside.)

ah, I had to subtract the two, 29.6 cm - 24.9 cm = 4.7 cm.

 

[haruspex]

ah, I had to subtract the two, 29.6 cm - 24.9 cm = 4.7 cm.

Yes.