Question

1.). Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 4.00 cm, a wavelength of 3.50 m, and a period of 6.25 s, but one has a phase shift of an angle φ. What is the phase shift (in rad) if the resultant wave has an amplitude of 4.00 cm? Hint: Use the trig identity

2.). Consider two sinusoidal sine waves traveling along a string, modeled as

y₁(x, t) = (0.2 m)sin[(6 m⁻¹)x − (4 s⁻¹)t]

and

y₁(x, t) = (0.2 m)sin[(6 m⁻¹)x + (4 s⁻¹)t].

What is the wave function of the resulting wave? (Hint: Use the trig identity

sin(u ± v) = sin(u) cos(v) ± cos(u) sin(v).

Use the following as necessary: x and t. Assume x and y are measured in meters and t is measured in seconds. Do not include units in your answer. Simplify your answer completely.)

3.) A transverse wave on a string is modeled with the wave function y(x, t) = (0.50 cm) sin

5.00 m⁻¹ x − 5.00 s⁻¹ t +

. What is the height of the string (in cm) with respect to the equilibrium position at a position

x = 3.00 m

and a time

t = 12.00 s?

(Include the sign of the value in your answer.)

4.) A copper wire has a density of

ρ = 8,920 kg/m³,

a radius of 1.40 mm, and a length L. The wire is held under a tension of 24.00 N. Transverse waves are sent down the wire.

a. What is the linear mass density of the wire (in kg/m)?

b. What is the speed of the waves through the wire (in m/s)?

Please respond to as many as possible. I have been trying for weeks. Thaanks!!!!!

Answer 1

as per guidelines i can write only one