A progressive sine wave of amplitude A and wavelength is moving with speed . Write down an expression for the vertical displacement of the wave at a position x along it at time if the frequency of the wave is

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is yR(x,t)=0.35cmsin(6.28m1x1.57s1t+4) . What are the period, wavelength, amplitude, and phase shift of the individual waves?

A traveling wave on a string is modeled by the wave equation y(x,t)=0.30msin(8.00m1x+100.00s1t) . The string is under a tension of 50.00 N and has a linear mass density of =0.008 kg/m. What is the average power transferred by the wave on the string?

The power versus time for a point on a string (=0.05kg/m) in which a sinusoidal traveling wave is induced is shown in the preceding figure. The wave is modeled with the wave equation y(x,t)=Asin(20.93m1x1t) . What is the frequency and amplitude of the wave?

A wave is modeled with the function y(x,t)=(0.25m)cos(0.30m1x0.90s1t+3) . Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) phase shift, (f) wavelength, and (g) period of the wave.

A pulse can be described as a single wave disturbance that moves through a medium. Consider a pulse that is defined at time t=0.00s by the equation y(s)=6.00m3x2+2.00m2 centered around x=0.00m . The pulse moves with a velocity of v=3.00m/s in the positive x-direction. (a) What is the amplitude of the pulse? (b) What is the equation of the pulse as a function of position and time? (c) Where is the pulse centered at time t=5.00s ?

Check Your Understanding The wave equation 2y(x,t)x2=1v22y(x,t)t2 works for any wave of the form y(x,t)=f(xvt) . In the previous section, we stated that a cosine function could also be used to model a simple harmonic mechanical wave. Check if the wave y(x,t)=0.50mcos(0.20m1x4.00s1t+10) is a solution to the wave equation. Any disturbance that complies with the wave equation can propagate as a wave moving along the x-axis with a wave speed v. It works equally well for waves on a string, sound waves, and electromagnetic waves. This equation is extremely useful. For example, it can be used to show that electromagnetic waves move at the speed of light.

Consider the wave function y(x,t)=(3.00cm)sin(0.4m1x+2.00s1t+10) . What are the period, wavelength, speed, and initial phase shift of the wave modeled by the wave function?

The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the ripple is 0.1 cm at a distance from the source of 6.00 meters, what was the amplitude at a distance of 2.00 meters from the source?

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is yR(x,t)=0.70msin(3.00m1x6.28s1t+/16rad) . What are the angular frequency, wave number, amplitude, and phase shift of the individual waves? .