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Chapter 17: Q. 38 (page 484)

Tendons are, essentially, elastic cords stretched between two fixed ends. As such, they can support standing waves. A woman has a 20-cm-long Achilles tendon—connecting the heel to a muscle in the calf—with a cross-section area of 90 mm2.. The density of tendon tissue is 1100 kg/m3. For a reasonable tension of 500 N, what will be the fundamental frequency of her Achilles tendon?

Short Answer

Expert verified

The fundamental frequency of the tendon is 177.5 Hz

Step by step solution

01

Write the given information 

The length of the tendon, L= 20 cm = 0.2m
Area of cross section, A= 90 mm2 = 90x 10-6 m2
The density of the tendon, ρ= 1100 kg/ m3
The tension in the string, T= 500N

02

To determine the fundamental frequency of tendon 

The mass per unit length of the string is given by
µ=ρA=(1100kg/m3)(90x10-6m2)=0.099kg/m

The frequency of the tendon is given by

f=12LTµ=12(0.2)500N0.099kg/m=2.5(71)=177.5Hz

Thus, the fundamental frequency of the tendon is 177.5 Hz

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Most popular questions from this chapter

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = r fn for all n. In this system, the frequency doubles every 12notes—an interval called an octave.

a. What is the value of r?

b. Orchestras tune to the note A, which has a frequency of440 Hz. What is the frequency of the next note of the scale (called A-sharp)?

Two loudspeakers emit sound waves along the x-axis. The

sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm.

a. What is the wavelength of the sound?

b. If the distance between the speakers continues to increase, at

what separation will the sound intensity again be a maximum?

A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes?

FIGURE EX17.27 shows the circular wave fronts emitted by two

wave sources.

a. Are these sources in phase or out of phase? Explain.

b. Make a table with rows labeled P, Q, and R and columns

labeled r1,r2,∆r,and C/D. Fill in the table for points P, Q, and

R, giving the distances as multiples of l and indicating, with a

C or a D, whether the interference at that point is constructive

or destructive.

An organ pipe is tuned to exactly 384 Hz when the room temperature is 20°C. If the room temperature later increases to 22°C, does the pipe’s frequency increase, decrease, or stay the same? Explain.

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