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NEED CORRECT ANSWERS FOR 5 STAR RATING. In the figure below, a string, tied to a

ID: 1314386 • Letter: N

Question

NEED CORRECT ANSWERS FOR 5 STAR RATING.

In the figure below, 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 = 1.19 m, linear density ? = 1.5 g/m, and the oscillator frequency f = 107 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) What mass m allows the oscillator to set up the fourth harmonic on the string?

INCLUDE UNITS

(b) What standing wave mode, if any, can be set up if m = 1.00 kg? (If no mode can be set up, enter NONE.)

Explanation / Answer


A) fourth harmonic frequency f4 = 4*107 = 428 Hz...

but f4 = (4/2L)*sqrt(T/mu)...
here T = tension in string = m*g...
and mu = linear density 1.5 g/m = 1.5*10^-3 kg/m...

L = 1.19m...

therefore 428 = (4/2*1.19)*sqrt(T/1.5*10^-3)...
(428*1.19)/2 = sqrt(T/1.5*10^-3).......
T = 97.278 N..
mg = 97.278...
m = 97.278/g = 97.278/9.8 = 9.92 kg....

B)fn = (n/2L)*sqrt(T/mu).....

107 = n/(2*1.19)*sqrt(9.8*1/1.5*10^-3)...

n = 9.92= 10 approximately