Passage
Sound waves propagate through many conducting structures in the ear before they are transduced into neuronal signals. When sound waves reach the fluid-filled cochlea, they are detected by hair cells lining the basilar membrane. The cochlear spiral can be modeled as a resonator system because each section of the basilar membrane is sensitive to a specific frequency (Figure 1) .
Figure 1 Amplitude pattern of the basilar membrane for different frequenciesPresbycusis (age-related hearing loss) results from a combination of factors that lessens an individual's mechanical and/or neurological sensitivity to sound. Pure tone audiometry (PTA) is used to determine an individual's ability to detect different sound frequencies and can be used to evaluate presbycusis. A "pure" tone is characterized by a single sinusoidal waveform. An audiogram plots the relative intensity required of a given frequency to be detected by the individual (Figure 2) .
Figure 2 Audiogram of an elderly patient exhibiting presbycusis
-The earliest stethoscope was simply a wooden pipe open at both ends. The fundamental frequency of a 0.25-m stethoscope will cause resonance at approximately what distance along the basilar membrane from its base? (Note: Use 350 m/s for the speed of sound in air.)

Question

Passage
Sound waves propagate through many conducting structures in the ear before they are transduced into neuronal signals. When sound waves reach the fluid-filled cochlea, they are detected by hair cells lining the basilar membrane. The cochlear spiral can be modeled as a resonator system because each section of the basilar membrane is sensitive to a specific frequency (Figure 1) .

Figure 1 Amplitude pattern of the basilar membrane for different frequenciesPresbycusis (age-related hearing loss) results from a combination of factors that lessens an individual's mechanical and/or neurological sensitivity to sound. Pure tone audiometry (PTA) is used to determine an individual's ability to detect different sound frequencies and can be used to evaluate presbycusis. A "pure" tone is characterized by a single sinusoidal waveform. An audiogram plots the relative intensity required of a given frequency to be detected by the individual (Figure 2) .

Figure 2 Audiogram of an elderly patient exhibiting presbycusis
-The earliest stethoscope was simply a wooden pipe open at both ends. The fundamental frequency of a 0.25-m stethoscope will cause resonance at approximately what distance along the basilar membrane from its base? (Note: Use 350 m/s for the speed of sound in air.)

Quizplus · Accepted Answer

11ecba2d_12ee_b06e_a3bf_15943d923917_MD0008_00 The resonant frequency of an object is the frequency that causes relatively large oscillations compared to other frequencies. The fundamental frequency is the lowest resonant frequency, and each subsequent harmonic frequency is a multiple of the fundamental frequency. Resonant frequency waves are known as standing waves because the locations of the nodes and antinodes do not change. Nodes occur at the locations of zero displacement, and antinodes occur at the locations of maximum displacement. The resonant frequency of a pipe depends on the length of the pipe and if the ends are closed. A closed end has a node (zero displacement) and an open end has an antinode (maximum displacement). The stethoscope is described as a pipe open at both ends for which the pipe's length is one half the wavelength of the fundamental frequency: 11ecba2d_12ee_b06f_a3bf_4537f039a000_MD0008_00 Therefore, the resonant wavelength is twice the given length L = 0.25 m of the stethoscope: 11ecba2d_12ee_d780_a3bf_d9675d239512_MD0008_00 From the wave velocity equation, the velocity v of a wave is the product of its wavelength λ and frequency f: 11ecba2d_12ee_d781_a3bf_c34eb03b2905_MD0008_00 Therefore, the frequency of the wave is the given speed of sound v = 350 m/s divided by λ = 0.5 m: 11ecba2d_12ee_d782_a3bf_6f7bade52e10_MD0008_00 From Figure 1, a frequency of 700 Hz would cause the basilar membrane to resonate around 25 mm from it base. (Choice D) For a pipe closed on one end, the pipe's length is one-fourth the wavelength of the fundamental frequency: L = λ/4. This wavelength corresponds to a frequency of 350 Hz (around 32 mm). Educational objective: For a pipe open at both ends, the length is half the fundamental frequency wavelength (L = λ/2). From the wave velocity equation (v = λf), frequency is calculated by dividing the wave's velocity by its wavelength.

Passage Sound Waves Propagate Through Many Conducting Structures in the Ear