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Chapter 17: Q7. (page 482)

In music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency f0. To increase the frequency by an octave, to 2f0, by what factor would you have to (a) increase the tension or (b) decrease the length?

Short Answer

Expert verified

a) 4 times

b) 2 times

Step by step solution

01

Given information

Frequency of guitar string is being doubled by keeping everything constant except for a) Tension, b) length.

02

Relation of frequency of a string to tension and length.

f=12LTsμ

03

Part a): Dependency on Tension

We can see frequency is directly proportional to square root of tension. So in order to increase frequency by 2 times we have to increase the tension in the string by 4 times.

04

Part b): Dependency on Length

We can see frequency is inversely proportional to the length of string, so to increase the frequency by 2 times, length has to be decrease by 2 times (or halved).

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Most popular questions from this chapter

A 1.0-m-tall vertical tube is filled with 20∘C water. A tuning fork vibrating at 580 Hz is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube above the water?

FIGURE EX17.15 shows a standing sound wave in an 80-cm-long tube. The tube is filled with an unknown gas. What is the speed of sound in this gas?

Traditional Indonesian music uses an ensemble called a gamelan that is based on tuned percussion instruments somewhat like gongs. In Bali, the gongs are often grouped in pairs that are slightly out of tune with each other. When both are played at once, the beat frequency lends a distinctive vibrating quality to the music. Suppose a pair of gongs are tuned to produce notes at 151 Hz and 155 Hz. How many beats are heard if the gongs are struck together and both ring for 2.5 s?

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.

FIGURE EX17.2 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s.
See all solutions

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