Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

The linear density of a string is $1.6 \times 10^{- 4} k g / m$ . A transverse wave on the string is described by the equation $y = (0.021 m) s i n [(2.0 m^{- 1}) x + (30 s^{- 1}) t]$ . (a)What are the wave speed and (b) What is the tension in the string?

a) The speed of the wave is 15m/s

b) The tension in the string is $3.60 \times 10^{- 3} N$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The wave equation is given as $y = (0.021 m) \sin [(2.0 m^{- 1}) x + (30 s^{- 1}) t]$
Linear density of a string, $(μ) = 1.6 \times 10^{- 4} kg / m$
Wavelength, $(λ) = 0.5 m$
Frequency, $(f) = 30 s^{- 1}$

Step 2: Understanding the concept of wave equation

The product of wavelength and frequency of the wave is called speed of the wave. the speed of the wave in a stretched string is directly proportional to the square-root of the tension force and inversely proportional to the square-root of linear density of the string.

Formula:

The wave speed of the wave, $v = n \times λ$ (i)

The velocity of the wave, $v = \sqrt{\frac{T}{μ}}$ (ii)

Step 3: a) Calculation of the wave speed

Using equation (i), the wave speed is given as:

$v = 30 s^{- 1} \times 0.5 m = 15 m / s$

Hence, the value of wave speed is 15 m/s

Step 4: b) Calculation of tension in the string

Using equation (ii), the tension in the string is given as:

$T = v^{2} μ = {(15 m / s)}^{2} \times (1.6 \times 10^{- 4} kg / m) = 3.60 \times 10^{- 3} N$

Hence, the value of the tension in the string is $3.60 \times 10^{- 3} N$ .

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Fundamentals Of Physics

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Short Answer

The linear density of a string is $1.6 \times 10^{- 4} k g / m$ . A transverse wave on the string is described by the equation $y = (0.021 m) s i n [(2.0 m^{- 1}) x + (30 s^{- 1}) t]$ . (a)What are the wave speed and (b) What is the tension in the string?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of wave equation

Step 3: a) Calculation of the wave speed

Step 4: b) Calculation of tension in the string

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The linear density of a string is 1.6×10-4kg/m. A transverse wave on the string is described by the equation y=(0.021m) sin[2.0m-1x+30s-1t]. (a)What are the wave speed and (b) What is the tension in the string?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of wave equation

Step 3: a) Calculation of the wave speed

Step 4: b) Calculation of tension in the string

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The linear density of a string is $1.6 \times 10^{- 4} k g / m$ . A transverse wave on the string is described by the equation $y = (0.021 m) s i n [(2.0 m^{- 1}) x + (30 s^{- 1}) t]$ . (a)What are the wave speed and (b) What is the tension in the string?