Ch16-p021 - 21(a We read the amplitude from the graph It is about 5.0 cm(b We read the wavelength from the graph The curve crosses y = 0 at about x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 21. (a) We read the amplitude from the graph. It is about 5.0 cm. (b) We read the wavelength from the graph. The curve crosses y = 0 at about x = 15 cm and again with the same slope at about x = 55 cm, so λ = (55 cm – 15 cm) = 40 cm = 0.40 m. (c) The wave speed is v = τ / μ , where τ is the tension in the string and μ is the linear mass density of the string. Thus, v= 3.6 N = 12 m/s. 25 ×10−3 kg/m (d) The frequency is f = v/λ = (12 m/s)/(0.40 m) = 30 Hz and the period is T = 1/f = 1/(30 Hz) = 0.033 s. (e) The maximum string speed is um = ωym = 2πfym = 2π(30 Hz) (5.0 cm) = 940 cm/s = 9.4 m/s. (f) The angular wave number is k = 2π/λ = 2π/(0.40 m) = 16 m–1. (g) The angular frequency is ω = 2πf = 2π(30 Hz) = 1.9×102 rad/s (h) According to the graph, the displacement at x = 0 and t = 0 is 4.0 × 10–2 m. The formula for the displacement gives y(0, 0) = ym sin φ. We wish to select φ so that 5.0 × 10–2 sin φ = 4.0 × 10–2. The solution is either 0.93 rad or 2.21 rad. In the first case the function has a positive slope at x = 0 and matches the graph. In the second case it has negative slope and does not match the graph. We select φ = 0.93 rad. (i) The string displacement has the form y (x, t) = ym sin(kx + ωt + φ). A plus sign appears in the argument of the trigonometric function because the wave is moving in the negative x direction. Using the results obtained above, the expression for the displacement is y ( x, t ) = ( 5.0 × 10−2 m ) sin (16 m −1 ) x + (190s −1 )t + 0.93 . ...
View Full Document

This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online