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$\bullet$ The equation describing a transverse wave on a string is$$y(x, t)=(1.50 \mathrm{mm}) \sin \left[\left(157 \mathrm{s}^{-1}\right) t-\left(41.9 \mathrm{m}^{-1}\right) x\right]$$Find (a) the wavelength, frequency, and amplitude of thiswave, (b) the speed and direction of motion of the wave, and(c) the transverse displacement of a point on the string when$t=0.100$ s and at a position $x=0.135 \mathrm{m} .$

a) 0.15$m$b) 3.75 $\mathrm{m} / \mathrm{s}$c) $-8.7 \times 10^{-4} m$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

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So we have a new equation for the position of the Y. So why of X? T equals 1.5 millimeters. This is simply the equation of a wave sign of 157 seconds to the negative first power Times T and then minus 41.9 meters to the negative First power times X and we're going. Teo, compare this to the general equation. This is equaling, eh? Sign of two pi times t divide about the period minus X divided by land of the wavelength. So we also know that velocity equals the wavelength times the frequency. So for part Ah, A When it's asking for the amplitude, the amplitude is simply going to be 1.50 millimetres, um, to find the wavelength. This is simply going to be equal to two pi divided by 41.9 and this is equaling 0.150 meters. And then for the period, this will simply be to pie divided by 157 and we're getting at the period is going to be Ah, now that we can say we can keep this as the period and then when we want to find the frequency. The frequency is simply the reciprocal of the period. So this will be 157 divided by two pi. And this is giving us 25.0 hurts. Ah, Part B is asking for the speed of the wave. So velocity equals Lambda Times. The frequency and the sole equal point 150 meters times 25.0 hurts. And this will equal 3.75 meters per second. And then this is in the positive ex direction. So this will be your answer for part B. This is your answer for Part II and then we had to find the frequency and the and the wavelength in order to find the propagation speed of the wave. And then lastly, part C is saying, What is the Y position? If X equals 0.135 meters and if time is and if 0.100 seconds have elapsed essentially and this will equal point zero 015 we're goingto convert 1.5 millimeters in two meters sign of 157 times point, um, one and then minus 41.9 times 0.1 35 uh, close parentheses and we find that why is going to be equal to Negative Point, Sirio 00 870 meters. So this will be our final answer for part C. That is the end of the solution. Thank you for watching.

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