Question

Oscillation of a 280 Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 630 m/s. The standing wave has four loops and an amplitude of 2.7 mm. (a) What is the length of the string? (b) Write an equation for the displacement of the string as a function of position and time. Round numeric coefficients to three significant digits. (a) Number Units ? Edit (b) y (x, t) Units

Answer 1

A)

Length, λ = v/f = 630/280 = 2.25 m

B)

k = 2π/λ = 2π /2.25 = 2.79 rad/m

Angular frequency, ω = 2πf = 2π x 280 = 1759.29 rad/sec

A = 2.7 mm

General equation is

y(x, t) = 2A sin(kx) cos(ωt)

y(x, t) = (5.4 mm) sin(2.79 x) cos(1759.29 t)

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