Wave motionMediumBloom L3
Question
A string of length L is fixed at one end and under tension due to a mass M = 25 kg hanging from the other end, as shown in the sketch. Coordinate axes are chosen so that the string runs from x = –L/2 to x = L/2, and y is the transverse displacement. The string is vibrating at one of its resonant frequencies with displacement:
y(x,t) = 0.05 cos(12.0x)sin(360t) ...(i)
with x, y in meters and t in seconds. What are the three smallest possible values of L consistent with equation (i)?
Options
A.λ, 2λ, 3λ
B.λ/2, 3λ/2, 5λ/2
C.λ/2, λ, 3λ/2
D.λ/4, λ/2, 3λ/4
Solution
Sol. From given equation, at x = 0, value of 0.05 cos(12x) is maximum, So x = 0 is an antinode.
So total no. of loops must be odd as shown:
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