The change in frequency when the length is doubled

Question

One string of a certain musical instrument is 74.0 cm long and has a mass of 8.76 g. It is being played in a room where the speed of sound is 344 m/s. To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.760 m ? (Assume that the breaking stress of the wire is very large and isn’t exceeded.) What frequency sound does this string produce in its fundamental mode of vibration?

Answer 1

Question

Chapter 14, Problem 2OQ

(a)

To determine

The change in frequency when the length is doubled

(b)

To determine

The change in frequency when the mass per unit length is doubled

(c)

To determine

The change in frequency when the tension is doubled

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One string of a certain musical instrument is 74.0 cm long and has a mass of 8.76 g. It is being played in a room where the speed of sound is 344 m/s. To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.760 m ? (Assume that the breaking stress of the wire is very large and isn’t exceeded.) What frequency sound does this string produce in its fundamental mode of vibration?

A string of length L, mass per unit length m, and tension T is vibrating at its fundamental frequency. (a) If the length of the string is doubled, with all other factors held constant, what is the effect on the fundamental frequency? It becomes four times larger.It becomes two times larger. It becomes √2 times larger.It is unchanged.It becomes 1/√2 times as large.It becomes one-half as large.It becomes one-fourth as large. (b) If the mass per unit length is doubled, with all other factors held constant, what is the effect on the fundamental frequency? It becomes four times larger.It becomes two times larger. It becomes √2 times larger.It is unchanged.It becomes 1/√2 times as large.It becomes one-half as large.It becomes one-fourth as large. (c) If the tension is doubled, with all other factors held constant, what is the effect on the fundamental frequency? It becomes four times larger.It becomes two times larger. It becomes √2 times larger.It is unchanged.It becomes 1/√2 times…

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