Question

A 0.800-m-long string with linear mass density m = 7.50 g>m is stretched between two supports. The string has tension F and a standing-wave pattern (not the fundamental) of frequency 624 Hz. With the same tension, the next higher standing-wave frequency is 780 HzWhat is the What is the frequency and wavelength of the fundamental standing wave for this string?

What is the value of F?

Answer 1

f=156Hz

F=467.25N

wavelength =1.6m

Step-by-step explanation:

we have two frequencies from the question 624hz and 780hz.

let them be f1 and f2

f1=624=nv/2L

f2=780=(n+1)v/2L

`(f1)/(f2)=624/780 =(n)/(n+1)`

624n+624=780n

n=4

velocity=2f1l/4

v=624*0.8/2

V=249.6m/s

The fundamental frequency of a wave is the following

f=v/2L

f=249.6/1.6

f=156hz

v=
`√(T/u)`

T=v^2u

=249.6^2*7.5*10^-3

T=467.25N

f=156Hz

T=467.25N

T=tension in the string

wavelength is

v=f w

w=249.6/156

w=1.6m