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Fundamentals Of Physics
Found in: Page 473

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Short Answer

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?

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

b) The tension in the string is 3.60×10-3N.

See the step by step solution

Step by Step Solution

Step 1: The given data

  • The wave equation is given as y=0.021msin2.0m-1x+30s-1t
  • Linear density of a string, μ=1.6×10-4kg/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.


The wave speed of the wave, v=n×λ (i)

The velocity of the wave,v=Tμ (ii)

Step 3: a) Calculation of the wave speed

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

v=30 s-1×0.5m =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=v2μ =15m/s2×1.6×10-4kg/m =3.60×10-3N

Hence, the value of the tension in the string is 3.60×10-3N.

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