A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation $y = 0.2 s i n (k x \pm ω t)$ . How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

1.9 ms

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3.9 ms

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2.4 ms

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0.5 ms

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Solution

The correct option is A 1.9 ms
$y = (0.2 m) s i n [k x \pm ω t] F o r x = 0, y = 0.1 m 0.1 = 0.2 s i n (ω t) \Rightarrow ω t = \frac{π}{6} o r \frac{5 π}{6} S o, t_{2} = \frac{5 π}{6 ω} a n d t_{1} = \frac{π}{6 ω} t_{2} - t_{1} = \frac{2 π}{3 ω} = \frac{1}{3 f} = 1.9 m s$

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Q. A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation

y = 0.2 s i n (k x \pm ω t)

. How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

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.