You want to measure the mass, m, of an object but you don?t have a scale. You th

Question

You want to measure the mass, m, of an object but you don?t have a scale. You therefore decide to attach the object to a string of mass, m, and length L, as in the figure and to generate standing waves on the string. The wave function which describes the standing wave is given by: where A is the wavelength, f is the frequency, and 4 is the phase. a) What value must have to have a node at the origin (x=0)? b) What is the wavelength, lambda 0, of the fundamental mode? c) if the fundamental frequency is f0, find the mass of the body.

Explanation / Answer

Velocity of the dtring = sqrt ( T/u )

u = m/L mass per unit length of string

T = Mg

V = sqrt ( Mg /u )

For fundamental frequency

wavelength lamda = L/4

we know that

V= f0 * lamda of fundamental frequency

V = f0 *L/4

f0 = 4V/L

f0 = 4sqrt ( Mg/u) /L

from above equation we have

(f0L)2/16 = MgL/m

f02Lm/16g = M

M =f02Lm/16g ( mass of block )

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