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Chapter 2: Q62P (page 501)

A vertical, \(1.20\;{\rm{m}}\) length of 18 gauge (diameter of 1.024 mm) copper wire has a 100.0 N ball hanging from it.

(a) What is the wavelength of the third harmonic for this wire?

(b) A 500.0 N ball now replaces the original ball. What is the change in the wavelength of the third harmonic caused by replacing the light ball with the heavy one? (Hint: Se Table 11.1 for Young鈥檚 modulus.)

Short Answer

Expert verified

Thus, (a) the wavelength of the third harmonic for the wire is 0.8 m

Step by step solution

01

(a) Given in the question

Tension in wire \(F = 100\;{\rm{N}}\).

Length of string \(L = 1.20\;m\)

Diameter of wire \(d = 1.024\;{\rm{mm}}\).

02

Use formula of wavelength

The formula of wavelength is:

\(\lambda = \frac{{2L}}{n}\).

Here,\(L\)length of string and\(n\)is harmonic number.

03

Calculate the wavelength

Solve the wavelength as follows:

\(\begin{array}{c}\lambda = \frac{{2L}}{n}\\ = \frac{2}{3} \times 1.2\\ = 0.8\;m\end{array}\)

Thus, the wavelength of the third harmonic for the wire is 0.8 m.

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Most popular questions from this chapter

Question:A 60.0-m-long brass rod is struck at one end. A person at the other end hears two sounds as a result of two longitudinal waves, one traveling in the metal rod and the other traveling in air. What is the time interval between the two sounds? (The speed of sound in air is 344 m/s; see Tables 11.1 and 12.1 for relevant information about brass.)

Interference of Triangular Pulses. Two triangular wave pulses are traveling toward each other on a stretched string as shown in Fig. E15.32. Each pulse is identical to the other and travels at \(2.00\;{{{\rm{cm}}} \mathord{\left/ {\vphantom {{{\rm{cm}}} {\rm{s}}}} \right. \\} {\rm{s}}}\). The leading edges of the pulses are \(1.00\;{\rm{cm}}\) apart at \(t = 0\). Sketch the shape of the string at \(t = 0.250\;{\rm{s}}\), \(t = 0.500\;{\rm{s}}\), \(t = 0.750\;{\rm{s}}\), \(t = 1.000\;{\rm{s}}\), and \(t = 1.250\;{\rm{s}}\)

Speed of Propagation vs. Particle Speed. (a) Show that Eq. (15.3) may be written as

\(y\left( {x,t} \right) = Acos\left[ {\frac{{2\pi }}{\lambda }\left( {x - vt} \right)} \right]\)

(b) Use \(y\left( {x,t} \right)\) to find an expression for the transverse velocity \({v_y}\)of a particle in the string on which the wave travels. (c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed \(v\) ? Less than\(v\)? Greater than\(v\)?

Question:What must be the stress (F/A) in a stretched wire of a material whose Young鈥檚 modulus is Yfor the speed of longitudinal waves to equal 30 times the speed of transverse waves?

Which of the following wave functions satisfies the wave equation, Eq. (15.12)? (a)\(y\left( {x,t} \right) = Acos\left( {kx + \omega t} \right)\) ; (b)\(y\left( {x,t} \right) = Asin\left( {kx + \omega t} \right)\) ; (c) \(y\left( {x,t} \right) = A\left( {coskx + cos\omega t} \right)\) (d) For the wave of part (b), write the equations for the transverse velocity and transverse acceleration of a particle at point x.

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