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One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 129 Hz. The other end passes over a pulley and supports a mass of 1.50 kg. The linear mass density of the rope is 0.0590 kg/m. What is the speed of a transverse wave on the rope? What is the wavelength? How would your answers to parts (a) and (b) be changed if the mass were increased to 2.80 kg?

Respuesta :

Answer:

(a). The speed of transverse wave on the rope is 15.78 m/s.

(b). The wavelength is 0.122 m.

(c). The changed speed of transverse wave on the rope is 21.56 m/s.

The changed wavelength is 0.167 m.

Explanation:

Given that,

Frequency = 129 Hz

mass = 1.50 kg

Linear mass density of the rope = 0.0590 kg/m

(a). We need to calculate the speed of a transverse wave on the rope

Using formula of speed

[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]

Put the value into the formula

[tex]v=\sqrt{\dfrac{1.50\times9.8}{0.0590}}[/tex]

[tex]v=15.78\ m/s[/tex]

(b). We need to calculate the wavelength

Using formula of wavelength

[tex]\lambda =\dfrac{v}{f}[/tex]

Put the value into the formula

[tex]\lambda=\dfrac{15.78}{129}[/tex]

[tex]\lambda=0.122\ m[/tex]

(c). If the mass were increased to 2.80 kg.

We need to calculate the speed of a transverse wave on the rope

Using formula of speed

[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]

Put the value into the formula

[tex]v=\sqrt{\dfrac{2.80\times9.8}{0.0590}}[/tex]

[tex]v=21.56\ m/s[/tex]

We need to calculate the wavelength

Using formula of wavelength

[tex]\lambda =\dfrac{v}{f}[/tex]

Put the value into the formula

[tex]\lambda=\dfrac{21.56}{129}[/tex]

[tex]\lambda=0.167\ m[/tex]

Hence, (a). The speed of transverse wave on the rope is 15.78 m/s.

(b). The wavelength is 0.122 m.

(c). The changed speed of transverse wave on the rope is 21.56 m/s.

The changed wavelength is 0.167 m.

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