A sinusoidal wave is traveling on a string with speed 4.0 cm/s. The displacement
ID: 1696276 • Letter: A
Question
A sinusoidal wave is traveling on a string with speed 4.0 cm/s. The displacement of the particles of the string at x = 20 cm is found to vary with time according to the equation y = (5.0 cm) sin[10.0 - (2.0 s-1)t]. The linear density of the string is 6.0 g/cm.(a) What is the frequency of the wave?
(b) What is the wavelength of the wave?
(c) Give the general equation giving the transverse displacement of the particles of the string as a function of position and time.
y(x,t) = ( ) sin[( )x - ( )t]
(d) What is the tension in the string?
Explanation / Answer
The given equation is in the form of
y = A sin [ kx - t ]
= (5cm) sin [10 - (2) t ]
Comparing the two equations
Here Kx = 10 and = 2.0
Frquency f = / 2
= 2 / 2
= 0.3183Hz
Wavelength = V / f
Given V = 4cm/s so
= 4 cm/ s / 0.3183
= 12.57cm
the propagation constant K = 10 / x = 10 / 20 = 0.5
The equation of the wave is
Y ( x, t) = (5cm) sin [ (0.5)x - (2) t ]
The speed of the wave is given as
V= [ T / m]
Here m is the linear density of the string.
Squaring and evaluating for tension is
T = V^2 m
= (4 x10^-2m/s)^2 (6x10^-1 kg / m)
= 24x10^-3 N