Wave Intensity Practice Problems

Scientists are experimenting with sound waves. They create two sound waves with the same frequency, one containing 4.0 times the energy of the other, and let them travel through the same point in the air. Calculate the ratio of the amplitudes of the two waves.

Engineers are conducting tests on a lighthouse. They measure the intensities of the light wave emitted from the lighthouse at two positions, 15 km and 25 km away. What is the ratio of the intensities at the two positions?

A group of students is trying to measure the ratio of the amplitudes of a spherical sound wave at 20 km and 30 km away from the source. Calculate the ratio.

A bug on the surface of a pond is observed to move up and down a total vertical distance of 0.20 m, lowest to highest point, as a wave passes. What is the amplitude of the wave?

A dragonfly on the surface of a lake moves up and down 0.12 m vertically, from the lowest to the highest point, as a wave passes. What is the change in the dragonfly's maximum kinetic energy if its amplitude increases to 0.17 m?

An ocean buoy moves up and down in response to passing waves, which can be approximated by a sinusoidal wave pattern. If the frequency of these waves is 0.40 Hz, what amplitude must the waves reach for the buoy to momentarily lose contact with the water surface? [Hint: The buoy will leave the water when the wave's acceleration exceeds 𝑔.]

A fire alarm system produces a loud sound that has an intensity of 5 × 10^-2 w/m² at a distance of 4 m. The alarm is on for 15 minutes. What is the energy transferred away from the alarm if its output power remains constant?

A loudspeaker emits sound waves uniformly in all directions. The intensity of the sound waves measured with a sound level meter at 10 m from the loudspeaker is 4 × 10^-8 W/m². What would be the intensity of the sound if you placed the sound level meter at 5 meters from the loudspeaker?

A powerful sound emitter is placed at the center of nuclear disposal to prohibit intrusion. The emitter sends sound waves uniformly in all directions. The minimum sound intensity at which an individual starts to feel pain is 1 W/m². If an intruder measures the intensity of 0.25 W/m² at 1 km, how close to the nuclear disposal could the intruder get before the noise became unbearable?

At 20 m from a portable generator, the sound intensity is 2 × 10^-4 W/m². The permissible noise intensity limit during the night is 0.5 μW/m².  i) At what distance from habitation should the generator be placed? ii) Calculate the intensity experienced by a person living at a distance twice the minimum distance. iii) What power of sound does the generator produce?

A light wave from a bulb has an intensity of 1.5 × 10^-2 W/m² at 25 m. Suppose the bulb radiates uniformly in all directions. Find the bulb's total power output.

A square solar collector with a side of 30.0 cm is used to charge batteries on Mars. Above Mars's atmosphere, solar electromagnetic radiation has an intensity of approximately 590 watts per square meter. Only 65% of the initial intensity reaches the solar collector. Calculate the amount of solar energy hitting the solar collector during 6.0 hours.

Lasers' high-precision welding features make them suitable to weld implantable medical devices. Pulsed Nd: YAG is typically used during the medical welding process. A pulsed Nd: YAG laser operates at a wavelength of 1064 nm with a typical pulse duration of 5 ns. Each laser pulse contains 2.0 joules. The laser spot radius is 0.75 mm. Calculate the intensity of the laser pulse.

A radio wave transmitter emits radio waves at an intensity of 4.5 × 10^-3 W/m². These waves are received by an antenna with a 120 cm diameter. Determine the amount of energy that will be delivered to the antenna if the radio waves are incident on the antenna for 3.0 min.

A car horn emits 50 W of sound power. Suppose you are standing 10.0 m away from the car. Determine the intensity of sound at the point where you are standing.

In a sound testing experiment, a loudspeaker is positioned on the horizontal axis. A sound wave of the same intensity could be heard simultaneously by the people standing at x = -12.0 m and x = 20.0 m along the horizontal axis. Determine the exact position of the loudspeaker on the horizontal axis.