Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

The equation of a transverse wave on a string is $y = (2.0 m m) s i n [(20 m^{- 1}) x - (600 s^{- 1}) t]$ . The tension in the string is 15 N . (a)What is the wave speed? (b)Find the linear density of this string in grams per meter.

a) The speed of the wave is $30 m / s$

b) The linear density of this string is $1.7 \times 10^{- 2} k g / m$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Equation of a transverse wave on a string is- $y = (2.0 m m) \sin [(20 m^{- 1}) x - (600 s^{- 1}) t]$
Tension in the string, T = 15 N
Angular frequency of the wave, $ω = 600 s^{- 1}$
Wavelength of the wave, $λ = 0.05 m$

Step 2: Understanding the concept of the wave equation

The product of the frequency and wavelength of the wave, gives us the wave speed. The linear density is the term used in place of the mass per unit length of the string.

Formula:

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

The formula for the linear density of distribution, $d = \frac{T}{v^{2}}$ (ii)

Step 3: a) Calculation for the wave speed

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

$v = 600 s^{- 1} \times 0.05 m = 30 m / s$

Hence, the value of the wave speed is

Step 4: b) Calculation of the linear density

Using equation (i) and the value of wave speed, we get the linear density as:

$d = \frac{15 N}{{(30 m / s)}^{2}} = 1.6667 \times 10^{- 2} k g / m \approx 1.7 \times 10^{- 2} k g / m$

Hence, the value of the linear density of the string is $1.7 \times 10^{- 2} k g / m$

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Fundamentals Of Physics

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Short Answer

The equation of a transverse wave on a string is $y = (2.0 m m) s i n [(20 m^{- 1}) x - (600 s^{- 1}) t]$ . The tension in the string is 15 N . (a)What is the wave speed? (b)Find the linear density of this string in grams per meter.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of the wave equation

Step 3: a) Calculation for the wave speed

Step 4: b) Calculation of the linear density

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The equation of a transverse wave on a string is y=(2.0 mm)sin[20 m-1x-600 s-1t] . The tension in the string is 15 N . (a)What is the wave speed? (b)Find the linear density of this string in grams per meter.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of the wave equation

Step 3: a) Calculation for the wave speed

Step 4: b) Calculation of the linear density

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The equation of a transverse wave on a string is $y = (2.0 m m) s i n [(20 m^{- 1}) x - (600 s^{- 1}) t]$ . The tension in the string is 15 N . (a)What is the wave speed? (b)Find the linear density of this string in grams per meter.