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3 years ago

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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 sp

eed of these waves be if the wire is replaced with one with the same length but three times as heavy

2 answers:

liubo4ka [24]3 years ago

4 0

Answer:

New speed of the wave, v = 5.77 m/s

Explanation:

It is given that,

Mass of the object, m = 5 kg

Length of the wire, L = 2 m

Speed of the wave, v = 10 m/s

The speed of wave in terms of tension is given by :

$v=\sqrt{\dfrac{T}{\mu}}$

$10=\sqrt{\dfrac{T}{\mu}}$

If the wire is replaced with one with the same length but three times as heavy, the mass per unit length is given by :

$\mu'=\dfrac{3m}{L}$

New speed of the wave is given by :

$v'=\sqrt{\dfrac{T}{\mu'}}$

$v'=\dfrac{1}{\sqrt{3} }\sqrt{\dfrac{T}{\mu}}$

$v'=\dfrac{10}{\sqrt{3} }$

v' = 5.77 m/s

So, the speed of the new wave is 5.77 m/s. Hence, this is the required solution.

Annette [7]3 years ago

4 0

The speed of these waves will be 5.8 m/s

$\texttt{ }$

<h3>Further explanation</h3>

Let's recall the speed of wave formula as follows:

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

<em>where:</em>

<em>c = speed of wave ( m/s )</em>

<em>λ = wavelength ( m )</em>

<em>f = frequency of wave ( Hz )</em>

$\texttt{ }$

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

<em>where:</em>

<em>v = speed of wave on string ( m/s )</em>

<em>T = tension in the string ( N )</em>

<em>μ = linear density ( kg/m )</em>

Let us now tackle the problem!

$\texttt{ }$

<u>Given:</u>

mass of the object = M = 5 kg

length of vertical wire = L = 2 m

initial speed of wave = v₁ = 10 m/s

initial mass of the wire = m₁ = m

final mass of the wire = m₂ = 3m

<u>Asked:</u>

final speed of wave = v₂ = ?

<u>Solution:</u>

$v_1 : v_2 = \sqrt{\frac{T}{\mu_1}} : \sqrt{\frac{T}{\mu_2}}$

$v_1 : v_2 = \sqrt{\mu_2} : \sqrt{\mu_1}$

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

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

$v_1 : v_2 = \sqrt{3m} : \sqrt{m}$

$10 : v_2 = \sqrt{3}$

$v_2 = 10 \div \sqrt{3}$

$v_2 = \frac{10}{3} \sqrt{3} \texttt{ m/s}$

$v_2 \approx 5.8 \texttt{ m/s}$

$\texttt{ }$

<h3>Learn more</h3>

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

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Wave

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