A sinusoidal wave is traveling on a string with speed 32.6 cm/s. The displacemen
ID: 1377550 • Letter: A
Question
A sinusoidal wave is traveling on a string with speed 32.6 cm/s. The displacement of the particles of the string at x = 15 cm is found to vary with time according to the equation
y = (2.4 cm) sin[2.3 - (5 s-1)t].
The linear density of the string is 4.0 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t) = ym sin(kx - ?t),
what are (c) ym, (d) k, and (e) ?, and (f) the correct choice of sign in front of ?? (g) What is the tension in the string?
Explanation / Answer
Solution: Comparing y = (2.4 cm) sin[2.3 - (5 s-1)t] with the standard equation given as y(x,t) = ym sin(kx - ?t), we get kx = 2.3, x = 15 cm, as k = 2?/?, ? = 40.95 cm (b).
? = 5 = 2?/T or, T = 1.256 sec. so, frequency n = 1/T = 0.796 Hz (a).
(c) ym = 2.4 cm, (d) k = 0.153 (e) ? = 5 rad/s (f) in the question there is '??' mark after 'in front of' (g) as v = (T/?)1/2, T = 4251 dyne.