16.4 Energy and Power of a Wave

Is the time-averaged power of a sinusoidal wave on a string proportional to the linear density of the string?

Consider a string with under tension with a constant linear mass density. A sinusoidal wave is produced by some external driving force. If the frequency, keeping the wave amplitude as it was originally, how is the time-averaged power of the wave affected? If the amplitude of the wave is decreased by half, keeping the wave frequency as it was originally, how is the time-averaged power affected? Exp…

In a transverse wave on a string, the motion of the string is perpendicular to the motion of the wave. If this is so, how is possible to move energy along the length of the string?

The intensity of a spherical waves decreases as the wave moves away from the source. If the intensity of the wave at the source is $I_{0} ,$ how far from the source will the intensity decrease by a factor of nine?

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 $y \left(x , t\right) = 0.01 \text{m} \text{sin} \left(15.7 \text{m}^{−1} x - 1170.12 \text{s}^{−1} t\right) .$ What is the power over one wavelength?

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 $0.1 \text{W}/\text{m}^{2}$?

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 $\text{W}/\text{m}^{2}$?

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

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

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?

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?