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.]

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]

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

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

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

the first wave is moving in positive x-direction

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