A wave traveling in the +x direction has an amplitude of 0.45 m, a speed of 6.1 m/s, and a frequency of 16 Hz. Write the equation of the wave in the form given by either Equation 16.3 or 16.4. (Answer in terms of t and x. Assume standard units.)
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Physics - drwls, Friday, April 27, 2007 at 1:00am
You have not provided the Equation forms mentioned.
16.3
v = square root(F/(m/L))
16.4
wave motion toward +x
y= A sin [(2(pi)(f)(t))- ((2(pi)(x))/lambda)]
I did it in terms of 16.4 and came up with an incorrect # three times.
To write the equation of the wave in the given form, we can use Equation 16.4:
y = A sin[(2πft) - (2πx/λ)]
Given information:
Amplitude (A) = 0.45 m
Speed (v) = 6.1 m/s
Frequency (f) = 16 Hz
We need to find the wavelength (λ) to complete the equation. The wavelength can be calculated using the formula:
v = λf
Substituting the known values:
6.1 m/s = λ * 16 Hz
Rearranging the equation, we get:
λ = 6.1 m/s / 16 Hz
Calculating the value:
λ ≈ 0.38125 m
Now we can substitute the values for A, f, and λ into the equation:
y = 0.45 sin[(2π * 16 * t) - (2π * x / 0.38125)]
This is the equation of the wave in the required form.