<< Chapter < Page Chapter >> Page >
  • Calculate the intensity and the power of rays and waves.
The destruction caused by an earthquake in Port-au-Prince, Haiti. Some buildings are shown on two sides of a street. Two buildings are completely destroyed. Rescue people are seen around.
The destructive effect of an earthquake is palpable evidence of the energy carried in these waves. The Richter scale rating of earthquakes is related to both their amplitude and the energy they carry. (credit: Petty Officer 2nd Class Candice Villarreal, U.S. Navy)

All waves carry energy. The energy of some waves can be directly observed. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls.

Loud sounds pulverize nerve cells in the inner ear, causing permanent hearing loss. Ultrasound is used for deep-heat treatment of muscle strains. A laser beam can burn away a malignancy. Water waves chew up beaches.

The amount of energy in a wave is related to its amplitude. Large-amplitude earthquakes produce large ground displacements. Loud sounds have higher pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large ocean breakers churn up the shore more than small ones. More quantitatively, a wave is a displacement that is resisted by a restoring force. The larger the displacement x size 12{x} {} , the larger the force F = kx size 12{F= ital "kx"} {} needed to create it. Because work W size 12{W} {} is related to force multiplied by distance ( Fx size 12{ ital "Fx"} {} ) and energy is put into the wave by the work done to create it, the energy in a wave is related to amplitude. In fact, a wave’s energy is directly proportional to its amplitude squared because

W Fx = kx 2 . size 12{W prop ital "Fx"= ital "kx" rSup { size 8{2} } } {}

The energy effects of a wave depend on time as well as amplitude. For example, the longer deep-heat ultrasound is applied, the more energy it transfers. Waves can also be concentrated or spread out. Sunlight, for example, can be focused to burn wood. Earthquakes spread out, so they do less damage the farther they get from the source. In both cases, changing the area the waves cover has important effects. All these pertinent factors are included in the definition of intensity     I size 12{I} {} as power per unit area:

I = P A size 12{I= { {P} over {A} } } {}

where P size 12{P} {} is the power carried by the wave through area A size 12{A} {} . The definition of intensity is valid for any energy in transit, including that carried by waves. The SI unit for intensity is watts per square meter ( W/m 2 size 12{"W/m" rSup { size 8{2} } } {} ). For example, infrared and visible energy from the Sun impinge on Earth at an intensity of 1300 W/m 2 size 12{"1300"`"W/m" rSup { size 8{2} } } {} just above the atmosphere. There are other intensity-related units in use, too. The most common is the decibel. For example, a 90 decibel sound level corresponds to an intensity of 10 3 W/m 2 size 12{"10" rSup { size 8{ - 3} } `"W/m" rSup { size 8{2} } } {} . (This quantity is not much power per unit area considering that 90 decibels is a relatively high sound level. Decibels will be discussed in some detail in a later chapter.

Calculating intensity and power: how much energy is in a ray of sunlight?

The average intensity of sunlight on Earth’s surface is about 7 00 W/m 2 size 12{7"00"`"W/m" rSup { size 8{2} } } {} .

(a) Calculate the amount of energy that falls on a solar collector having an area of 0 . 500 m 2 size 12{0 "." "500"`"m" rSup { size 8{2} } } {} in 4 . 00 h size 12{4 "." "00"`"h"} {} .

(b) What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200 times smaller than its own?

Strategy a

Because power is energy per unit time or P = E t size 12{P= { {E} over {t} } } {} , the definition of intensity can be written as I = P A = E / t A size 12{I= { {P} over {A} } = { { {E} slash {t} } over {A} } } {} , and this equation can be solved for E with the given information.

Solution a

  1. Begin with the equation that states the definition of intensity:
    I = P A . size 12{I= { {P} over {A} } } {}
  2. Replace P size 12{P} {} with its equivalent E / t size 12{E/t} {} :
    I = E / t A . size 12{I= { { {E} slash {t} } over {A} } } {}
  3. Solve for E size 12{P} {} :
    E = IAt . size 12{E= ital "IAt"} {}
  4. Substitute known values into the equation:
    E = 700 W/m 2 0 . 500 m 2 4 . 00 h 3600 s/h . size 12{E= left ("700"" W/m" rSup { size 8{2} } right ) left (0 "." "500"" m" rSup { size 8{2} } right ) left [ left (4 "." "00"" h" right ) left ("3600"" s/h" right ) right ]} {}
  5. Calculate to find E size 12{E} {} and convert units:
    5 . 04 × 10 6 J , size 12{5 "." "04" times "10" rSup { size 8{6} } "J"} {}

Discussion a

The energy falling on the solar collector in 4 h in part is enough to be useful—for example, for heating a significant amount of water.

Strategy b

Taking a ratio of new intensity to old intensity and using primes for the new quantities, we will find that it depends on the ratio of the areas. All other quantities will cancel.

Solution b

  1. Take the ratio of intensities, which yields:
    I I = P / A P / A = A A ( The powers cancel because P = P ) .
  2. Identify the knowns:
    A = 200 A , size 12{A="200"A'} {}
    I I = 200 . size 12{ { {I rSup { size 8{'} } } over {I} } ="200"} {}
  3. Substitute known quantities:
    I = 200 I = 200 700 W/m 2 . size 12{I'="200"I="200" left ("700"`"W/m" rSup { size 8{2} } right )} {}
  4. Calculate to find I size 12{I'} {} :
    I = 1.40 × 10 5 W/m 2 . size 12{ { {I}} sup { ' }=1 "." "40" times "10" rSup { size 8{5} } `"W/m" rSup { size 8{2} } } {}

Discussion b

Decreasing the area increases the intensity considerably. The intensity of the concentrated sunlight could even start a fire.

Got questions? Get instant answers now!

Questions & Answers

what is heat
John Reply
Heat is a form of energy where molecules move
Can you please help me with some questions
Janet Reply
topic-- question
I know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.
Jake Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian Reply
why is a body moving at a constant speed able to accelerate
Lilian Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
because it changes only direction and the speed is kept constant
Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
why is the north side is always referring to n side of magnetic
sam Reply
who is a nurse
Chilekwa Reply
A nurse is a person who takes care of the sick
a nurse is also like an assistant to the doctor
explain me wheatstone bridge
Malik Reply
good app
Wheatstone bridge is an instrument used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
Rockwell Software is Rockwell Automation’s "Retro Encabulator". Now, basically the only new principle involved is that instead of power being generated by the relative motion of conductors and fluxes, it’s produced by the modial interaction of magneto-reluctance and capacitive diractance. The origin
what refractive index
Adjah Reply
write a comprehensive note on primary colours
Harrison Reply
relationship between refractive index, angle of minimum deviation and angle of prism
Practice Key Terms 1

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?