The speed of these waves will be 14 m/s
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Further explanation
Let's recall the speed of wave formula as follows:
[tex]\boxed {v = \lambda \times f}[/tex]
where:
c = speed of wave ( m/s )
λ = wavelength ( m )
f = frequency of wave ( Hz )
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[tex]\boxed {v = \sqrt{\frac{T}{\mu}}}[/tex]
where:
v = speed of wave on string ( m/s )
T = tension in the string ( N )
μ = linear density ( kg/m )
Let us now tackle the problem!
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Given:
initial mass = m₁ = 5 kg
length of vertical wire = L = 2 m
initial speed of wave = v₁ = 10 m/s
final mass = m₂ = 2m₁ = 2(5) = 10 kg
Asked:
final speed of wave = v₂ = ?
Solution:
[tex]v_1 : v_2 = \sqrt{\frac{T_1}{\mu}} : \sqrt{\frac{T_2}{\mu}}[/tex]
[tex]v_1 : v_2 = \sqrt{T_1} : \sqrt{T_2}[/tex]
[tex]v_1 : v_2 = \sqrt{w_1} : \sqrt{w_2}[/tex]
[tex]v_1 : v_2 = \sqrt{m_1 g} : \sqrt{m_2 g}[/tex]
[tex]v_1 : v_2 = \sqrt{m_1} : \sqrt{m_2}[/tex]
[tex]10 : v_2 = \sqrt{5} : \sqrt{10}[/tex]
[tex]v_2 = 10\sqrt{2} \texttt{ m/s}[/tex]
[tex]v_2 \approx 14 \texttt{ m/s}[/tex]
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Learn more
- Frequency of Sound Wave : https://brainly.com/question/12441470
- Frequency of Beats : https://brainly.com/question/12367463
- Amplitude of Sound Wave : https://brainly.com/question/2675676
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
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Answer details
Grade: High School
Subject: Physics
Chapter: Wave
