Question

When a mass of 5 kg hangs from a vertical wire of length 2 m, waves travel on this wire with a speed of 10 m/s. What will the speed of these waves be, if the mass is doubled without stretching the wire?
14 m/s
20 m/s
5.0 m/s
12 m/s

Answer 1

Answer:

its 14 m/s

Explanation:

Answer 2

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:

$\boxed {v = \lambda \times f}$

where:

c = speed of wave ( m/s )

λ = wavelength ( m )

f = frequency of wave ( Hz )

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$\boxed {v = \sqrt{\frac{T}{\mu}}}$

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:

$v_1 : v_2 = \sqrt{\frac{T_1}{\mu}} : \sqrt{\frac{T_2}{\mu}}$

$v_1 : v_2 = \sqrt{T_1} : \sqrt{T_2}$

$v_1 : v_2 = \sqrt{w_1} : \sqrt{w_2}$

$v_1 : v_2 = \sqrt{m_1 g} : \sqrt{m_2 g}$

$v_1 : v_2 = \sqrt{m_1} : \sqrt{m_2}$

$10 : v_2 = \sqrt{5} : \sqrt{10}$

$v_2 = 10\sqrt{2} \texttt{ m/s}$

$v_2 \approx 14 \texttt{ m/s}$

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Learn more

• Frequency of Sound Wave : brainly.com/question/12441470
• Frequency of Beats : brainly.com/question/12367463
• Amplitude of Sound Wave : brainly.com/question/2675676

• Kinetic Energy : brainly.com/question/692781

• Acceleration : brainly.com/question/2283922

• The Speed of Car : brainly.com/question/568302

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Answer details

Grade: High School

Subject: Physics

Chapter: Wave