A metallic rod of length 1 m is rigidly clamped at its end points. Longitudinal stationary waves are setup in the rod in such a way that there are six antinodes of displacement wave observed along the rod. The amplitude of the antinode is 2 
10 -6 m. Write the equations of the stationary wave and the component waves at the point 0.1 m from the one end of the rod.
[Young's modulus = 7.5 
10 10 N/m 2 , density = 2500 kg/m 3 ]
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
V = 
= 
= 
= 1
λ = 
m
n = 
= 
ω = 2 π n
= 
a = 2 × 10 –6 m
for stationary wave y = a sin k x cos ( ω t + θ )
y = 2 × 10 –6 sin 6 π x cos (6 
π × 10 3 t + θ)
at x = 0.1
y = 2 × 10 –6 sin 
cos (6 
π × 10 3 t + θ)
y (0.1, t) = 2 × 10 –6 sin 
cos (6 
π × 10 3 t + θ)
y 1 (x, t) = 1 × 10 –6 sin (6 π x + 6 
π × 10 3 t + θ 1 )
y 2 (x, t) = 1 × 10 –6 sin (6 π x – 6 
π × 10 3 t + θ 2 )
at x = 0.1
y 1 (0.1, t) = 1 × 10 –6 sin ( 
+ 6 
π × 10 3 t + θ 1 )
y 2 (0.1, t) = 1 × 10 –6 sin ( 
– 6 
π × 10 3 t + θ 2 )
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