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In the figure, a string, tied to a sinusoidal oscillator at P and running over a

ID: 2242412 • Letter: I

Question

In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 0.9 m, linear density ? = 1.7 g/m, and the oscillator frequency f = 120 Hz. The amplitude of the motion at P is small enough fro that point to be considered a node. A node also exist at Q.

(A) What mass m allows the oscillator to set up the fourth harmonic montion on the string?

(b) Wht standing wave mode if any can be sat up if m= 1kg( Give 0 if the mass cannot set up a standign wave)?

In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 0.9 m, linear density ? = 1.7 g/m, and the oscillator frequency f = 120 Hz. The amplitude of the motion at P is small enough fro that point to be considered a node. A node also exist at Q. What mass m allows the oscillator to set up the fourth harmonic mention on the string? What standing wave mode if any can be sat up if m= 1kg( Give 0 if the mass cannot set up a standing wave)?

Explanation / Answer

As we know that


Frequency = (n/2L)*sqrt(T/u)


For Fourth Harmonics , n = 4


Therefore


120 = (4/(2*0.9))sqrt((m*9.8)/(1.7*10^-3))


m = 0.5058 Kg



For m = 1 Kg



120 = (n/(2*0.9))sqrt((1*9.8)/(1.7*10^-3))




m = 2.844


So 0 mass cannot set up a standign wave