Answer:
so tension in the string is 57.199 N
Explanation:
given data
long = 1.91 m
mass = 19.3 g
oscillated = 440 Hz
wavelength = 17.1 cm = 0.171 m
to find out
tension in the string
solution
we know equation
v = √(T/u) ...............................1
here
v = oscillation × wavelength = 440 × 0.171 = 75.24 m/s
and u = mass / length = 0.0193 / 1.91 = 0.010104712
so from equation 1
v = √(T/u)
75.24 = √(T/0.010104)
T = 57.199 N
so tension in the string is 57.199 N
When the string is vibrated, then the wave formed causes a tension force. Then the tension acting on the string is of 57.20 N.
When a string is stretched by applying some magnitude of force, then the string also applies the same amount of force in opposite direction. This force in opposite direction is known as tension force.
Given data:
The length of string is, L = 1.91 m.
The mass of string is, m = 19.3 g = 0.0193 kg.
The frequency of string is, f = 440 Hz.
The wavelength of transverse wave is, [tex]\lambda = 17.1\;\rm cm =0.171 \;\rm m[/tex].
The mathematical expression for the velocity of wave travel along the string is given as,
[tex]v = \sqrt{\dfrac{T \times L}{m}}[/tex]
Here,
T is the tension in the string.
The wave velocity is also expressed as,
[tex]v = f \times \lambda\\\\v = 440 \times 0.171\\\\v = 75.24 \;\rm m/s[/tex]
Then the tension in the string is calculated as,
[tex]75.24 = \sqrt{\dfrac{T \times 1.91}{0.0193}}\\\\T =57.20 \;\rm N[/tex]
Thus, we can conclude that the tension acting on the string is of 57.20 N.
Learn more about the tension force here:
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