Question

Transverse waves on a string have wave speed amplitude 0.0700 m, and wavelength 0.320 m. (a) Find the frequency, period, and wave number of these waves. (b) Write the equation for describing these waves. (c) Find the transverse displacement of a point on the string at time.

a. (a) f = 5.0 Hz, T = 0.20 s, k = 19.6 m⁻¹; (b) y(x, t) = 0.0700 sin(19.6t - 2πx/0.320); (c) y(0.150 m, 0.040 s) = 0.035 m

b. (a) f = 3.1 Hz, T = 0.32 s, k = 12.5 m⁻¹; (b) y(x, t) = 0.0700 sin(12.5t - 2πx/0.320); (c) y(0.150 m, 0.040 s) = 0.035 m

c. (a) f = 5.0 Hz, T = 0.20 s, k = 19.6 m⁻¹; (b) y(x, t) = 0.0700 cos(19.6t - 2πx/0.320); (c) y(0.150 m, 0.040 s) = 0.035 m

d. (a) f = 3.1 Hz, T = 0.32 s, k = 12.5 m⁻¹; (b) y(x, t) = 0.0700 cos(12.5t - 2πx/0.320); (c) y(0.150 m, 0.040 s) = 0.035 m

Answer 1

The frequency, period, and wave number can be found using the wave speed and wavelength. The wave function can be written if phase constant information is provided, and the displacement can only be determined with the wave function specified.

Step-by-step explanation:

To answer the student's question, we must use the wave equation which relates wave speed (v), frequency (f), wave number (k), amplitude, and wavelength (λ). The general wave equation is y(x, t) = A sin(kx - ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, φ is the phase constant, and k is the wave number. Given a wave speed of 30.00 m/s and a wavelength of 0.320 m, we can solve for the following:

• The frequency f is the speed divided by the wavelength, giving f = v / λ.
• The period T is the reciprocal of the frequency, or T = 1 / f.
• The wave number k is given by k = 2π / λ.

For part (b) and (c), you would need specific information about the phase constant and the wave function to write the equation and determine the displacement at a certain position and time.