A mass is hung from the end of a string with linear density 1.8 g/m around a sma

Question

A mass is hung from the end of a string with linear density 1.8 g/m around a small fric- tionless peg. For some values of this mass the string resonates with the vibrator’s frequency and develops visible standing waves. A vibra- tor of constant frequency 155 Hz is attached near one end of the string of vibrating length 2 m. 2m = 1.8 g/m Answer in units of m. 155 Hz m vibrator What is the largest mass that will produce a standing wave of any wavelength in the string shown in the figure? The acceleration of gravity is 9.8 m/s2 . Answer in units of kg.

Explanation / Answer

Let : L = 2 m ,
f = 127 Hz , and
µ = 1.8 g/m = 0.0018 kg/m .

so L =/2
and
v = f = sqrt Fr/µ

f (2 L) = sqrt m g/µ

m = 4f^2*L^2 µ/g

= 4 (2 m)2*(155 Hz)^2*(0.0018 kg/m)/9.8 m/s^2

m = 35.30kg

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