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Answer:
a. 282.84 cm/s b. 100 cm/s c. 400 cm/s d. 200 cm/s
Explanation:
The speed of the wave v = √(T/μ) where T = tension and μ = mass per unit length = m/l where m = mass of string and l = length of string.
So, v = √(T/μ)
v = √(T/m/l)
v = √(Tl/m)
a. The string's tension is doubled?
If the tension is doubled, T' = 2T the new speed is
v' = √(T'l/m)
v' = √(2Tl/m)
v' = √2(√Tl/m)
v' = √2v
v' = √2 × 200 cm/s
v' = 282.84 cm/s
b. The string's mass is quadrupled (but its length is unchanged)?
If the mass is quadrupled, m' = 4m the new speed is
v' = √(Tl/m')
v' = √(Tl/4m)
v' = (1/√4)(√Tl/m)
v' = v/2
v' = 200/2 cm/s
v' = 100 cm/s
c. The string's length is quadrupled (but its mass is unchanged)?
If the length is quadrupled, l' = 4l the new speed is
v' = √(Tl'/m)
v' = √(T(4l)/m)
v' = √4)(√Tl/m)
v' = 2v
v' = 200 × 2 cm/s
v' = 400 cm/s
d. The string's mass and length are both quadrupled?
If the length is quadrupled, l' = 4l and mass quadrupled, m' = 4m, the new speed is
v' = √(Tl'/m')
v' = √(T(4l)/4m)
v' = √(Tl/m)
v' = v
v' = 200 cm/s