Astring attached to an oscillator at one end forms 5 nodes (counting the two ends) and produces a frequency of ν = 1.5 khz. the string is l = 1.2 m long and is under a tension of t = 276 n.

what is the linear density of the string, in kilograms per meter?

Explanation:

The order of the harmonics for standing waves in a string is equal to the number of nodes minus 1, so

n = 5 - 1 = 4

In this case, the frequency of the 4th-harmonic is

We also know the relationship between the frequency of the nth-harmonic and the fundamental frequency:

so we find the fundamental frequency:

The fundamental frequency is given by

where

L = 1.2 m is the length of the string

T = 276 N is the tension in the string

is the linear density

Solving the equation for , we find

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explanation:

fgravity=10x10=100n case 1

fgravity=30x20=600n case 2

6 times more