To write an expression describing a transverse wave traveling along a string, we can use the general form of a wave equation. The equation describes the displacement of the wave as a function of position (x) and time (t).
The general form of a transverse wave equation is:
y(x, t) = A * sin(kx - ωt + φ)
where:
- y(x, t) is the displacement of the wave at position x and time t,
- A is the amplitude of the wave,
- k is the wave number (2π divided by the wavelength),
- ω is the angular frequency (2π times the frequency), and
- φ is the phase constant.
Given: Wavelength (λ) = 11.4 cm Frequency (f) = 385 Hz Amplitude (A) = 2.13 cm
To find the wave number (k), we use the formula: k = 2π / λ
Substituting the given values: k = 2π / 11.4 cm
To find the angular frequency (ω), we use the formula: ω = 2πf
Substituting the given values: ω = 2π * 385 Hz
Now, we can write the expression for the transverse wave:
y(x, t) = A * sin(kx - ωt + φ)
Substituting the known values: y(x, t) = 2.13 cm * sin((2π / 11.4 cm) * x - (2π * 385 Hz) * t + φ)
Note that the phase constant (φ) is not specified in the given information. If you have a specific phase constant value, you can include it in the expression. Otherwise, you can omit it or set it to zero.