13-2: Sound Intensity and Resonance Objectives: Calculate the intensity of sound waves. Relate intensity, decibel level, and perceived loudness. Explain why resonance occurs. Intensity vs. loudness Sound intensity is objective and is measured by instruments. Intensity is the rate at which energy flows through a unit area perpendicular to the direction of wave motion Loudness, on the other hand, is a physiological sensation sensed in the brain. Intensity Because power, P, is defined as the rate of energy transfer, intensity can also be described in terms of power. Intensity = Intensity The SI unit for power is the watt. Thus, intensity has units of watts per square meter (W/m 2 ). In a spherical wave, energy propagates equally in all directions; no one direction is preferred over any other. In this case, the power emitted by the source (P) is distributed over a spherical surface (area = 4pr 2 ), assuming that there is no absorption in the medium. Intensity in a Spherical Wave Intensity = We use the area of a sphere for the denominator. What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the power output of the trumpet is 0.20 W? Assume that the sound waves are spherical. Given: P = 0.20 W r = 3.2 m Unknown: Intensity = ?, Intensity= Intensity and frequency determine which sounds are audible The frequency of sound waves heard by the average human ranges from 20 to 20,000 Hz. The softest sounds that can be heard by the average human ear occur at a frequency of about 1000 Hz and an intensity of 1.0 10 12 W/m 2. (watts/meter 2 ) The loudest sounds that the human ear can tolerate have an intensity of about 1.0 W/m 2. Relative Intensity Relative intensity, which is found by relating the intensity of a given sound wave to the intensity at the threshold of hearing, corresponds more closely to human perceptions of loudness. Relative intensity is also referred to as decibel level because relative intensity is measured in units called decibels (dB). Sounding boards are an important part of all stringed musical instruments because they are forced into vibration and produce the sound. An unmounted tuning fork makes a faint sound. Strike a tuning fork while holding its base on a tabletop, and the sound is relatively loud because the table is forced to vibrate. Its larger surface sets more air in motion. A forced vibration occurs when an object is made to vibrate by another vibrating object that is nearby. Forced Vibration The vibration of guitar strings in an acoustical guitar would be faint if they werent transmitted to the guitars wooden body. The mechanism in a music box is mounted on a sounding board. Without the sounding board, the sound the music box mechanism makes is barely audible. Forced Vibration When the string is plucked, the washtub is set into forced vibration and serves as a sounding board. Forced Vibration Why are sounding boards an important part of stringed instruments? Forced Vibration An object resonates when there is a force to pull it back to its starting position and enough energy to keep it vibrating. Resonance If the frequency of a forced vibration matches an objects natural frequency, resonance dramatically increases the amplitude. You pump a swing in rhythm with the swings natural frequency. Timing is more important than the force with which you pump. Even small pumps or pushes in rhythm with the natural frequency of the swinging motion produce large amplitudes. Resonance If two tuning forks are adjusted to the same frequency, striking one fork sets the other fork into vibration. Each compression of a sound wave gives the prong a tiny push. The frequency of these pushes matches the natural frequency of the fork, so the pushes increase the amplitude of the forks vibration. The pushes occur at the right time and are repeatedly in the same direction as the instantaneous motion of the fork. Resonance a.The first compression gives the fork a tiny push. b.The fork bends. c.The fork returns to its initial position. d.It keeps moving and overshoots in the opposite direction. e.When it returns to its initial position, the next compression arrives to repeat the cycle. Resonance If the forks are not adjusted for matched frequencies, the timing of pushes will be off and resonance will not occur. When you tune a radio, you are adjusting the natural frequency of its electronics to one of the many incoming signals. The radio then resonates to one station at a time. Resonance Resonance occurs whenever successive impulses are applied to a vibrating object in rhythm with its natural frequency. The Tacoma Narrows Bridge collapse was caused by resonance. Wind produced a force that resonated with the natural frequency of the bridge. Amplitude increased steadily over several hours until the bridge collapsed. Tacoma Narrows Bridge Collapse Resonance The human ear