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Chapter 2: Q28E (page 539)

The Vocal Tract. Many opera singers (and some pop singers) have a range of about21/2 octaves or even greater. Suppose a soprano’s range extends from A below middle C (frequency 220 Hz) up to E-flat above high C (frequency 1244 Hz). Although the vocal tract is quite complicated, we can model it as a resonating air column, like an organ pipe, that is open at the top and closed at the bottom. The column extends from the mouth down to the diaphragm in the chest cavity, and we can also assume that the lowest note is the fundamental. How long is this column of air if v = 354 m/s? Does your result seem reasonable, on the basis of observations of your own body?

Short Answer

Expert verified

The length of the air column in the vocal tract is 0.39 m.

Step by step solution

01

STEP 1 Concept of the frequency of standing wave in a stopped pipe

A pipe which has a closed end is given by

f=nv4L

where,f is the frequency of nth harmonic, v is the velocity of the wave, nrepresents the number ofharmonic (n — 1, 3, 5, ...), L is the length of the pipe.

02

Calculate the length of the column

The frequency of thenth harmonic is given by the formula-

f=nv4LL=nv4f=1×344m/s4×220Hz=0.39m

Therefore, the length of the column is 0.39 m.

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Most popular questions from this chapter

A loud factory machine produces sound having a displacement amplitude of 1.00 μ-m, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maxi mum pressure amplitude of the sound waves is limited to 10.0 Pa. Under the conditions of this factory, the bulk modulus of air is 1.42 x 105 Pa. What is the highest-frequency sound to which this machine can be adjusted without exceeding the prescribed limit? Is this frequency audible to the workers?

In most modern wind instruments the pitch is changed by

using keys or valves to change the length of the vibrating air column.

The bugle, however, has no valves or keys, yet it can play many notes. How might this be possible? Are there restrictions on what notes a bugle can play?

The sound source of a ship’s sonar system operates at a frequency of 18.0 kHz. The speed of sound in water (assumed to be at a uniform 20°C) is 1482 m>s. (a) What is the wavelength of the waves emitted by the source? (b) What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling directly toward the ship at 4.95 m/s? The ship is at rest in the water.

Does an aircraft make a sonic boom only at the instant its speed exceeds Mach 1? Explain.

Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone. For what frequencies does their sound at the speakers produce (a) constructive interference and (b) destructive interference?
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