1)The resultant wave from the interference of two identical waves traveling in opposite directions is described by the wave function y(x, t) = (2.49 m)sin(0.0458x)cos(5.40t), where

x and y are in meters and t is in seconds. a) What is the frequency of the two interfering waves? What is the wavelength of the two interfering waves? (c) What is the speed of the two interfering waves?

To answer these questions, we need to understand the wave function provided. The wave function given is y(x, t) = (2.49 m)sin(0.0458x)cos(5.40t).

(a) Frequency:
To find the frequency of the interfering waves, we need to identify the angular frequency (ω) from the equation. The angular frequency is given by the coefficient of the variable 't' in the equation.
In this case, the angular frequency is 5.40 rad/s.

To find the frequency (f), we can use the formula:
ω = 2πf

Rearranging the formula, we have:
f = ω / 2π

Substituting the value of ω, we get:
f = 5.40 rad/s / (2π)

Evaluating this expression, we find that the frequency of the interfering waves is approximately 0.859 Hz.

(b) Wavelength:
The wavelength is related to the wave number (k) by the formula:
k = 2π / λ

where λ is the wavelength.

Comparing the given equation to the general form of a wave equation, y(x, t) = A sin(kx - ωt), we can equate the wave number (k) to 0.0458.

Using the formula for wave number, we have:
0.0458 = 2π / λ

Rearranging the formula, we can solve for the wavelength (λ):
λ = 2π / 0.0458

Evaluating this expression, we find that the wavelength of the interfering waves is approximately 137.69 m.

(c) Speed:
The speed of a wave can be found by multiplying the frequency (f) by the wavelength (λ):
v = fλ

Substituting the values of f and λ, we have:
v = 0.859 Hz * 137.69 m

Evaluating this expression, we find that the speed of the interfering waves is approximately 118.23 m/s.

To find the frequency of the two interfering waves, we can look at the equation for the wave function:

y(x, t) = (2.49 m) sin(0.0458x) cos(5.40t)

The frequency of a wave is given by the coefficient in front of the time variable. In this case, the coefficient is 5.40. Therefore, the frequency of the two interfering waves is 5.40 Hz.

To find the wavelength of the two interfering waves, we can use the formula:

wavelength = speed / frequency

The speed of the wave can be found by taking the derivative of the displacement function with respect to time and using the equation:

speed = frequency * wavelength

Taking the derivative of y(x, t) with respect to t, we get:

dy/dt = -2.49 m * sin(0.0458x) * sin(5.40t)

Using the equation for the speed of the wave, we have:

speed = 5.40 Hz * wavelength

Equating the two expressions for the speed, we can solve for the wavelength:

-2.49 m * sin(0.0458x) * sin(5.40t) = 5.40 Hz * wavelength

From this equation, we can see that the wavelength is dependent on x and t, which means it can vary depending on the values of x and t.

Therefore, the wavelength of the two interfering waves is not constant and cannot be determined without specific values for x and t.