Find the fundamental frequency and the next three frequencies that could cause standing-wave patterns on a string that is 30.0 m long, has a mass per length of 9.00 - 10#3 kg/m, and is stretched to a tension of 20.0 n.

0.786 Hz, 1.572 Hz, 2.358 Hz, 3.144 Hz

Explanation:

The fundamental frequency of a standing wave on a string is given by

where

L is the length of the string

T is the tension in the string

is the mass per unit length

For the string in the problem,

L = 30.0 m

T = 20.0 N

Substituting into the equation, we find the fundamental frequency:

The next frequencies (harmonics) are given by

with n being an integer number and f being the fundamental frequency.

So we get:

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