One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at $120 H z$ . The other end passes over a pulley and supports a $1.50 k g$ mass. The linear mass density of the rope is $0.0750 k g / m$ . The speed of a transverse wave on the rope is $1.41 \times 10^{x} m / s$ . Find the value of $x$ .

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Solution

Speed of transverse wave in a rope= $\sqrt{\frac{T}{μ}}$
$= \sqrt{\frac{1.5 \times 10}{0.0750}} \approx 14.1 m / s$

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Q. One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at

120 H z

. The other end passes over a pulley and supports a

1.50 k g

mass. The linear mass density of the rope is

0.0550 k g / m

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One end of a long string of linear mass density $8.0 \times 10^{- 3}$ kg $m^{- 1}$ is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.