In the arrangement shown below, an object of mass m =2.0 kg hangs from a cord ar

Question

In the arrangement shown below, an object of mass m =2.0 kg hangs from a cord around a lightpulley. The length of the cord between point P and thepulley is L = 2.0 m. (a) When the vibrator is set to a frequency of145 Hz, a standing wave with six loops isformed. What must be the linear mass density of the cord? (b) How many loops (if any) will result ifm is changed to 18.0 kg?
(c) How many loops (if any) will result if m is changed to4.50 kg?
In the arrangement shown below, an object of mass m =2.0 kg hangs from a cord around a lightpulley. The length of the cord between point P and thepulley is L = 2.0 m. (a) When the vibrator is set to a frequency of145 Hz, a standing wave with six loops isformed. What must be the linear mass density of the cord? (b) How many loops (if any) will result ifm is changed to 18.0 kg?
(c) How many loops (if any) will result if m is changed to4.50 kg?
(a) When the vibrator is set to a frequency of145 Hz, a standing wave with six loops isformed. What must be the linear mass density of the cord? (b) How many loops (if any) will result ifm is changed to 18.0 kg?
(c) How many loops (if any) will result if m is changed to4.50 kg?

Explanation / Answer

we know that v = f and v (Tension/ mass density) thus (Tension/ mass density) = f = 2m / 3waves = .666 meters f = 145Hz T = mass x gravity = 2 * 9.8 = 19.6N 19.6N/ mass density = (.666 x 145)2 mass density = 19.6 / 9326 = .00203 kg/m2 (b) (18*9.8/.00203) = f 295 = 145 = 2m so two loops will form (b) (4.5*9.8/.00203) = f 147 = 145 = 1m so four loops will be formed because 2 loops form one wavelengthand there are 2 wavelengths on th elengths of cord if anything is unclear message me and I will be happy to clarifythe answer.

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