In Fig. 16-45, a string, tied to a sinusoidal oscillator at \( P \) and running over a support a...

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In Fig. 16-45, a string, tied to a sinusoidal oscillator at \( P \) and running over a support at \( Q \), is stretched by a block of mass \( m \). The separation \( L \) between \( P \) and \( Q \) is \( 1.20 \mathrm{~m} \), and the frequency \( f \) of the oscillator is fixed at \( 120 \mathrm{~Hz} \). The amplitude of the motion at \( P \) is small enough for that point to be considered a node. A node also exists at \( Q \). A standing wave appears when the mass of the hanging block is \( 286.1 \mathrm{~g} \) or \( 447.0 \mathrm{~g} \), but not for any intermediate mass. What is the linear density of the string?
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