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An elastic cord that is 4.21 m long has a mass of 0.0204 kg. What tension must be applied to the cord to make the wavelength of a 112 Hz wave 1.135 m?

Answer :

77.4 N of tension must be applied to the rope in order to create a 112 Hz wave's wavelength 1.135 m.

What is the meaning of wavelength?

The distance that separates the crests and troughs of the light wave is known as the wavelength of light. With the Greek letter lambda (λ), it is identified. As a result, wavelength refers to the separation between one wave's peak or dip and the following wave.

The wave equation may be used to connect the cord's tension to the wave's wavelength and frequency:

v = fλ

where,

v denotes the wave's speed

The frequency is f, and

The wavelength is λ

The elastic cord's elastic wave's velocity is provided by:

v = √(T/μ)

where,

T is the cord's tension, and

μ is the cord's linear mass density,

This is the mass per unit length:

μ = m/L

where m is the cord's mass and

Its length is L.

When we solve for the tension T using these formulas in the wave equation, we obtain:

T = μv² = μ(fλ)²

Inputting the values provided yields:

μ = m/L = 0.0204 kg / 4.21 m = 0.00484 kg/m

v = √(T/μ) --> v² = T/μ

λ = v/f --> v = λ*f

T = μv² = μ(fλ)²

= (0.00484 kg/m)*(1.135 m * 112 Hz)²

= 77.4 N

Hence, 77.4 N of tension must be applied to the rope in order to create a 112 Hz wave's wavelength 1.135 m.

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