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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鈥攃onnecting the heel to a muscle in the calf鈥攚ith 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, 蚁= 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
碌=蚁A=(1100kg/m3)(90x10-6m2)=0.099kg/m

The frequency of the tendon is given by

f=12LT碌=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

As the captain of the scientific team sent to Planet Physics, one

of your tasks is to measure g. You have a long, thin wire labeled

1.00 g/m and a 1.25 kg weight. You have your accurate space cadet

chronometer but, unfortunately, you seem to have forgotten a

meter stick. Undeterred, you first find the midpoint of the wire by

folding it in half. You then attach one end of the wire to the wall

of your laboratory, stretch it horizontally to pass over a pulley at

the midpoint of the wire, then tie the 1.25 kg weight to the end

hanging over the pulley. By vibrating the wire, and measuring

time with your chronometer, you find that the wire鈥檚 second harmonic

frequency is 100 Hz. Next, with the 1.25 kg weight still

tied to one end of the wire, you attach the other end to the ceiling

to make a pendulum. You find that the pendulum requires 314 s to

complete 100 oscillations. Pulling out your trusty calculator, you

get to work. What value of g will you report back to headquarters?

FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz. a. How many antinodes will there be if the frequency is increased to 200 Hz? b. If the tension is increased by a factor of 4, at what frequency will the string continue to oscillate as a standing wave that looks like the one in the figure?

An open-open organ pipe is 78.0 cm long. An open-closed pipe has a fundamental frequency equal to the third harmonic of the open-open pipe. How long is the open-closed pipe?

A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string鈥檚 linear density is 0.600 g/m and the tension is 150 N, how long is the vibrating section of the violin string?

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,鈭�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

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