Answer:
(a) Wavelength is 0.436 m
(b) Length is 0.872 m
(c) 11.518 m/s
Solution:
As per the question:
The eqn of the displacement is given by:
(1)
n = 4
Now,
We know the standard eqn is given by:
(2)
Now, on comparing eqn (1) and (2):
A = 1.22 cm
K = 

where
A = Amplitude
K = Propagation constant
= angular velocity
Now, to calculate the string's wavelength,
(a) 
where
K = propagation vector


(b) The length of the string is given by:


(c) Now, we first find the frequency of the wave:



Now,
Speed of the wave is given by:


Answer: 50π m ≈ 157 m
Explanation:
100 rev/min (2π rad/rev) / (60 sec/min) = 3⅓π rad/s
d = ωrt = 3⅓π(0.50)(30) = 50π m ≈ 157 m
the electrons should be in the outer valence levels/shells.