Question

The crest of a Parasaurolophus dinosaur skull is shaped somewhat like a trombone and contains a nasal passage in the form of a long, bent tube open at both ends. The dinosaur may have used the passage to produce sound by setting up the fundamental mode in it. (a) If the nasal passage in a certain Parasaurolophus fossil is 2.0 m long, what frequency would have been produced? (b) If that dinosaur could be recreated (as in Jurassic Park), would a person with a hearing range of 60 Hz to 20 kHz be able to hear that fundamental mode and, if so, would the sound be high or low frequency? Fossil skulls that contain shorter nasal passages are thought to be those of the female Parasaurolophus. (c) Would that make the female's fundamental frequency higher or lower than the male's?

Answer 1

Hint: The number of times a repeated event occurs per unit of time is known as frequency. It's also known as temporal frequency, which stresses the difference between spatial and angular frequency. The unit of frequency is hertz (Hz), which equals one occurrence per second. Hence the formula of fundamental frequency is used.

Formula used:
\[f = \dfrac{{nv}}{{2L}}\]
V = velocity
L = length

Complete step-by-step solution:
The term frequency is defined as the number of cycles or vibrations per unit of time for cyclical phenomena such as oscillations, waves, or simple harmonic motion examples. f; is also used as a standard symbol for frequency. The period T is the amount of time it takes for an oscillation to complete one cycle. The lowest frequency of a periodic waveform is specified as the fundamental frequency, sometimes known as the fundamental frequency. The fundamental is the musical pitch of a note regarded as the lowest partial existent in music. The fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between nearby frequencies, in terms of a superposition of sinusoids.
We know that for v=343 $m{s^{ - 1}}$ and n=1,
The fundamental frequency in a nasal channel of length L=2.0 m is \[f = \dfrac{{nv}}{{2L}} = 86Hz\](subject to various assumptions about the nature of the passage as a "bent tube open at both ends").
(b) The sound would be audible as sound (rather than merely vibration) at a very low frequency.
(c) The formula above states that a smaller L equals a greater f. As a result, the female's voice has a higher pitch (frequency).
Women talk at a higher tone than males, around an octave higher. The typical range for an adult woman is 165 to 255 Hz, whereas for a guy it is 85 to 155 Hz. The rush of testosterone generated during adolescence leads men's vocal chords to extend and thicken, resulting in a deeper voice. Thicker, longer vocal cords produce a deeper sound, similar to the strings of a cello. "The female voice is actually more complex than the male voice, due to differences in the size and shape of the vocal cords and larynx between men and women, as well as women having greater natural melody in their voices. In comparison to a male voice, this results in a more complicated range of sound frequencies.

Note:Make wise use of the formula. Do not use the $f = \dfrac{1}{T}$formula.
Males tend to speak in a low-pitched tone, whereas females speak in a high-pitched tone. Male voices are frequently linked with rougher articulation, whilst female voices are frequently linked with milder articulation. Males prefer to employ the entire pitch range while speech, whereas females vary the pitch range.