SHOW WORK PLEASE!!! In the figure, string 1 and string 2 have the same length L
ID: 1542998 • Letter: S
Question
SHOW WORK PLEASE!!!
In the figure, string 1 and string 2 have the same length L from the wall to the wheel, however, in that length, string 1 has mass mi and string 2 has mass m_2. Both strings are under tension owing to the hanging block of mass M [figure (a)]. Remember to write your answers in terms of the input parameters L, m_1 m_2, and M. a) What is the frequency of the fundamental harmonic produced by standing waves on string 1? b) The block is now divided into two blocks (with M_1 + M_2 = M) and the apparatus rearranged as shown in Figure (b). Find the values of M_1 and M_2 such that the two strings produce the same sound. c) What is the frequency of the sound produced with the arrangement described in part (c)? d) What is the average energy transported by the standing waves generated in each string?Explanation / Answer
(a) let say the tension in the string is T
therefore 2T = mg
T = mg/2
For string 1
frequency = v/2L
where v is velocity = (T/u)1/2 where u is the linear density = m1/ l1
frequency in string 1 = (1/2l1)(T/(m1 /l1))1/2
Similarly for the string 2 = (1/2l2)(T/(m2 /l2))1/2
(b) If they produce the same sound then frquency must be same
on equating the two , we get
m1l1 = m2l2
Since m1 + m2 = M
therefore m1 + m1l1 /l2 = M
m1 = M*l2 / (l1 + l2)
m2 = M*l1 / (l1 + l2)
(c) in this case in first string T = m1g
and for string 2 , T = m2g
(d) Average energy = (1/2)Luw2 where w is the frequency in rad/s
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