The wavelength of the standing wave at fourth harmonic is; λ = 0.985 m and the frequency of the wave at the calculated wavelength is; f = 36.84 Hz
Given Conditions:
mass of string; m = 0.0133 kg
Force on the string; F = 8.89 N
Length of string; L = 1.97 m
1. To find the wavelength at the fourth normal node.
At the fourth harmonic, there will be 2 nodes.
Thus, the wavelength will be;
λ = L/2
λ = 1.97/2
λ = 0.985 m
2. To find the velocity of the wave from the formula;
v = √(F/(m/L)
Plugging in the relevant values gives;
v = √(8.89/(0.0133/1.97)
v = 36.2876 m/s
Now, formula for frequency here is;
f = v/λ
f = 36.2876/0.985
f = 36.84 Hz
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Joules is a unit for work which may decomposed into N.m. Work is a quantity which is a product of force (in this case, the woman's weight) and the distance she has traveled.
W = F x d ; d = W / F
Substituting the given,
d = (3.5 x 10^4 J) / (55 kg x 9.8 m/s²) = 64.94 m
Thus, the woman can climb up to 64.94 meters.
Answer:
Focal length, f = 16 cm
Explanation:
Image distance, v = 24 cm
Object distance, u = -48 cm
We need to find the focal length of the lens. It can be determined using the lens formula as :
f = 16 cm
So, the focal length of the converging lens is 16 cm. Hence, this is the required solution.
