第16章波動

A string of length 5 m and a mass of 90 g is held under a tension of 100 N. A wave travels down the string that is modeled as $y\left(x,t\right)=0.01\text{m}\text{sin}\left(15.7{\text{m}}^{\mathrm{-1}}x-1170.12{\text{s}}^{\mathrm{-1}}t\right).$ What is the power over one wavelength?

Ultrasound of intensity $1.50\times {10}^2{\text{W/m}}^2$ is produced by the rectangular head of a medical imaging device measuring 3.00 cm by 5.00 cm. What is its power output?

The low-frequency speaker of a stereo set has a surface area of $A=0.05{\text{m}}^2$ and produces 1 W of acoustical power. (a) What is the intensity at the speaker? (b) If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity $0.1{\text{W/m}}^2$?

To increase the intensity of a wave by a factor of 50, by what factor should the amplitude be increased?

A device called an insolation meter is used to measure the intensity of sunlight. It has an area of $100{\text{cm}}^2$ and registers 6.50 W. What is the intensity in ${\text{W/m}}^2$?

Energy from the Sun arrives at the top of Earth’s atmosphere with an intensity of $1400{\text{W/m}}^2$. How long does it take for $1.80\times {10}^9\text{J}$ to arrive on an area of $1.00{\text{m}}^2$?

Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device produces 10.0 kW of power on a day when the breakers are 1.20 m high, how much will it produce when they are 0.600 m high?

A photovoltaic array of (solar cells) is $10.0\text{\%}$ efficient in gathering solar energy and converting it to electricity. If the average intensity of sunlight on one day is $70.00{\text{W/m}}^2$, what area should your array have to gather energy at the rate of 100 W? (b) What is the maximum cost of the array if it must pay for itself in two years of operation averaging 10.0 hours per day? Assume that it earns money at the rate of 9.00 cents per kilowatt-hour.

A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally $2.00\times {10}^{\mathrm{-5}}{\text{W/m}}^2$, but is turned up until the amplitude increases by $30.0\text{\%}$, what is the new intensity?

A string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and a sinusoidal wave with an amplitude of 2.00 cm is induced on the string, what must the frequency be for an average power of 100.00 W?

The power versus time for a point on a string $\left(\mu =0.05\text{kg/m}\right)$ in which a sinusoidal traveling wave is induced. The wave is modeled with the wave equation $y\left(x,t\right)=A\text{sin}\left(20.93{\text{m}}^{\mathrm{-1}}x-\omega t\right)$. What is the frequency and amplitude of the wave?

A string is under tension $F_{T1}$. Energy is transmitted by a wave on the string at rate $P_1$ by a wave of frequency $f_1$. What is the ratio of the new energy transmission rate $P_2$ to $P_1$ if the tension is doubled?

A 250-Hz tuning fork is struck and the intensity at the source is $I_1$ at a distance of one meter from the source. (a) What is the intensity at a distance of 4.00 m from the source? (b) How far from the tuning fork is the intensity a tenth of the intensity at the source?

A sound speaker is rated at a voltage of $V=120.00\text{V}$ and a current of $I=10.00\text{A}.$ Electrical power consumption is $P=IV$. To test the speaker, a signal of a sine wave is applied to the speaker. Assuming that the sound wave moves as a spherical wave and that all of the energy applied to the speaker is converted to sound energy, how far from the speaker is the intensity equal to $3.82{\text{W/m}}^2?$

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?