Consider the following equations for two different traveling waves: I. y(x, t) =
ID: 1559461 • Letter: C
Question
Consider the following equations for two different traveling waves:
I. y(x, t) = (1.90 cm) sin [(6.20 cm1)x (7.30 s1)t]
II. y(x, t) = (4.15 cm) sin [(3.20 cm1)x + (2.90 s1)t]
(a) Which wave has the fastest wave speed? [(Select one) Wave 2, Both have the same speed, Wave 1]
What is that speed? Answer in cm/s.
(b) Which wave has the longest wavelength? [(Select one) Wave 1, Both have the same speed, Wave 2]
What is that wavelength? Answer in cm.
(c) Which wave has the fastest maximum speed of a point in the medium? [(Select one) Wave 2, Wave 1, both have the same maximum speed]
What is that speed? answer in cm/s.
(d) Which wave is moving in the positive x-direction? [(Select one) Both, Wave 1, Wave 2, Neither.]
Explanation / Answer
The wave equation for a wave travelling along positive x-direction is
y(x, t) = (A) * sin [(k)x (omega)t]
A is amplitude
k is wave number
omega is angular frequency
y(x, t) = (1.90 cm) sin [(6.20 cm1)x (7.30 s1)t]
y(x, t) = (4.15 cm) sin [(3.20 cm1)x + (2.90 s1)t]
a)
The first wave has fastest wave speed
the wave speed is given by
v = k * omega
for wave 1, v = 6.2 * 7.3 = 45.26 m/s
for wave 2, v = 3.2 * 2.9 = 9.28 m/s
b)
The second wave has the longest wavelength
the wave length is given by
lambda = 2pi / k
for second wave
lambda = 2pi / 3.2
lambda = 1.96 cm
c)
the maximum speed is given by
V = A * omega
for wave 1 , V = 1.9 * 7.3 = 13.87 cm/s
for wave 2 , V = 4.15 *2.9 = 12.035 cm/s
so the first wave has maximum speed
d)
the first wave is moving in positive x-direction