16.6 Standing waves and resonance  (Page 9/17)

Shown below is the plot of a wave function that models a wave at time $t=0.00\text{s}$ and $t=2.00\text{s}$ . The dotted line is the wave function at time $t=0.00\text{s}$ and the solid line is the function at time $t=2.00\text{s}$ . Estimate the amplitude, wavelength, velocity, and period of the wave.

The speed of light in air is approximately $v=3.00\times {10}^8\text{m/s}$ and the speed of light in glass is $v=2.00\times {10}^8\text{m/s}$ . A red laser with a wavelength of $\lambda =633.00\text{nm}$ shines light incident of the glass, and some of the red light is transmitted to the glass. The frequency of the light is the same for the air and the glass. (a) What is the frequency of the light? (b) What is the wavelength of the light in the glass?

A radio station broadcasts radio waves at a frequency of 101.7 MHz. The radio waves move through the air at approximately the speed of light in a vacuum. What is the wavelength of the radio waves?

A sunbather stands waist deep in the ocean and observes that six crests of periodic surface waves pass each minute. The crests are 16.00 meters apart. What is the wavelength, frequency, period, and speed of the waves?

A tuning fork vibrates producing sound at a frequency of 512 Hz. The speed of sound of sound in air is $v=343.00\text{m/s}$ if the air is at a temperature of $20.00\text{°}\text{C}$ . What is the wavelength of the sound?

A motorboat is traveling across a lake at a speed of $v_b=15.00\text{m/s}.$ The boat bounces up and down every 0.50 s as it travels in the same direction as a wave. It bounces up and down every 0.30 s as it travels in a direction opposite the direction of the waves. What is the speed and wavelength of the wave?

Use the linear wave equation to show that the wave speed of a wave modeled with the wave function $y\left(x,t\right)=0.20\text{m}\text{sin}\left(3.00{\text{m}}^{\mathrm{-1}}x+6.00{\text{s}}^{\mathrm{-1}}t\right)$ is $v=2.00\text{m/s}.$ What are the wavelength and the speed of the wave?

Given the wave functions $y_1\left(x,t\right)=A\text{sin}\left(kx-\omega t\right)$ and $y_2\left(x,t\right)=A\text{sin}\left(kx-\omega t+\varphi \right)$ with $\varphi \ne \frac{\pi }{2}$ , show that $y_1\left(x,t\right)+y_2\left(x,t\right)$ is a solution to the linear wave equation with a wave velocity of $v=\sqrt{\frac{\omega }{k}}.$

A transverse wave on a string is modeled with the wave function $y\left(x,t\right)=0.10\text{m}\text{sin}\left(0.15{\text{m}}^{\mathrm{-1}}x+1.50{\text{s}}^{\mathrm{-1}}t+0.20\right)$ . (a) Find the wave velocity. (b) Find the position in the y -direction, the velocity perpendicular to the motion of the wave, and the acceleration perpendicular to the motion of the wave, of a small segment of the string centered at $x=0.40\text{m}$ at time $t=5.00\text{s}.$

A sinusoidal wave travels down a taut, horizontal string with a linear mass density of $\mu =0.060\text{kg/m}.$ The magnitude of maximum vertical acceleration of the wave is $a_{y\text{max}}=0.90{\text{cm/s}}^2$ and the amplitude of the wave is 0.40 m. The string is under a tension of $F_T=600.00\text{N}$ . The wave moves in the negative x -direction. Write an equation to model the wave.

A transverse wave on a string $\left(\mu =0.0030\text{kg/m}\right)$ is described with the equation $y\left(x,t\right)=0.30\text{m}\text{sin}\left(\frac{2\pi }{4.00\text{m}}\left(x-16.00\frac{\text{m}}{\text{s}}t\right)\right).$ What is the tension under which the string is held taut?