BIO (a) ?Music?. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequency as the note that is sung. If someone sings the note B flat, which has a frequency of 466 Hz, how much time does it take the person’s vocal cords to vibrate through one complete cycle, and what is the angular frequency of the cords? (b) ?Hearing. When sound waves strike the eardrum, this membrane vibrates with the same frequency as the sound. The highest pitch that young humans can hear has a period of 50.0 µs. What are the frequency and angular frequency of the vibrating eardrum for this sound? (c) Vision. When light having vibrations with angular frequency ranging from 2.7 X 1015 rad/s to 4.7 X 1015 rad/s strikes the retina of the eye, it stimulates the receptor cells there and is perceived as visible light. What are the limits of the period and frequency of this light? (d) ?Ultrasound. High-frequency sound waves (ultrasound) are used to probe the interior of the body, much as x rays do. To detect small objects such as tumors, a frequency of around 5.0 MHz is used. What are the period and angular frequency of the molecular vibrations caused by this pulse of sound?
Solution 1E Step 1: (a).given frequency f = 466 Hz The time period is given by the equation T = 1/f = 1/466 Hz = 0.0021 s. Angular frequency of cords is given by w = 2f w = 2/T w = 2/0.0021 s w = 2991.99 Hz Step 2: (b). Time period T = 50 s Frequency is inversely proportional to time period.so frequency is given by f = 1/T f = 1/50 × 106 s f = 20000 Hz Angular frequency w = 2f w = 2/T w = 2/50 × 10 6 5 w = 125680 Hz or 1.25 × 10 rad/s