Question

the four strings of a bass guitar are 0.865 m long and are tuned to the notes g (98 hz), d (73.4 hz), a (55 hz), and e (41.2 hz). in one bass guitar, the g and d strings have a linear mass density of 4.8 g/m, and the a and e strings have a linear mass density of 29.8 g/m.what is the total force exerted by the strings on the neck?​

Answer 1

Answer: Total force = 636,554.55N

Explanation: To determine tension of strings, wave speed on a string is necessary. Speed is found by:

v = f.λ

f is frequency

λ is wavelength

For the strings, wavelength equals to:

$\lambda = 2L$

L is the length of the bass guitar string

Then, wave speed:

$v=f.2L$

Tension on a string is

$v=\sqrt{\frac{F_{T}}{\mu} }$

$v^{2}=\frac{{F_{T}} }{\mu}$

$F_{T} = v^{2}\mu$

$F_{T} = (2f\lambda)^{2}\mu$

$F_{T} = 4(f\lambda)^{2}\mu$

μ is linear mass density

For g string:

$F_{T} = 4(98.0.865)^{2}.4.8$

$F_{T}$ = 137970.3N

For d string:

$F_{T} = 4(73.4.0.865)^{2}.4.8$

$F_{T}=$ 77397.25N

For a string:

$F_{T} = 4(55.0.865)^{2}.29.8$

$F_{T}=$ 269795N

For e string:

$F_{T} = 4(41.2.0.865)^{2}.29.8$

$F_{T}=$ 151392N

Total force = 137,970.3 + 77,397.25 + 269,795 + 151,392

Total force = 636,554.55N

Total force exerted on the neck by the strings is 636,554.55N.