A sinusoidal wave is traveling on a string with speed 53.6 cm/s. The displacemen
ID: 1477356 • Letter: A
Question
A sinusoidal wave is traveling on a string with speed 53.6 cm/s. The displacement of the particles of the string at x = 12 cm is found to vary with time according to the equation
y = (7.6 cm) sin[1.5 - (6.7 s-1)t].
The linear density of the string is 2.7 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
the given equation:
y = (7.6 cm) sin[1.5 - (6.7 s-1)t]
the general wave equation:
y(x,t) = ym sin(kx - t),
compare the above two equations, we get
ym = 7.6 cm, k = 1.5, = 6.7 s-1
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a.
the frequency is calculated as follows:
f = /2 = 6.7/2* = 1.066 Hz
the wavelength of the wave:
= 2/k = 2/1.5 = 4.19 cm
the tension in the string:
v = sqrt[T/m/L]
T = V^2*(m/L) = 0.536*0.536 *2.7x10-3/10-2 = 0.0776 N