A string, which is fixed at point $P,$ is stretched by a block with mass $m$ at point $Q,$ as shown in the above figure. Point $P$ is generating a sinusoidal wave but the amplitude of $P$ is small enough to be considered as a node. The distance between $P$ and $Q$ is $L=1.50\text{ m},$ and the linear density of the string is $\mu=1.60\text{ g/m}.$ If the oscillating frequency of $P$ is $f=130\text{ Hz}$ and is setting up sixth harmonic on the string, what is the approximate mass $m$ of the block?

Assumptions and Details

• The gravitational acceleration is $g=9.80\text{ m/s}^2.$