   Chapter 14, Problem 64P

Chapter
Section
Textbook Problem

The G string on a violin has a fundamental frequency of 196 Hz. It is 30.0 cm long and has a mass of 0.500 g. While this string is sounding, a nearby violinist effectively shortens the G string on her identical violin (by sliding her finger down the string) until a beat frequency of 2.00 Hz is heard between the two strings. When that occurs, what is the effective length of her string?

To determine
The effective length of the violinist string.

Explanation

Given Info: The fundamental frequency of the G string on a violin is 196 Hz and beat frequency is 2.00Hz .

Formulae to calculate the fundamental frequency is,

f=f1+fbeat

• f is the fundamental frequency of the second violinist
• f1 is the fundamental frequency of the G string on a violin,
• fbeat is the beat frequency,

Substitute 196 Hz for f1 and 2.00 Hz for fbeat .

f=196Hz+2.00Hz=198Hz

While the string is sounding, a nearby violinist have shortens the G string on her identical violin. Since the speed of the transverse waves have the same value for both strings.

The relation between frequency and wavelength for G string on a violin is,

v1=λ1f1 (1)

• v1 is the speed of the transverse waves formed in a G string on a violin,
• λ1 is the wavelength of waves in G string on a violin,
• f1 is the frequency of the waves,

The relation between frequency and wavelength for violinist violin is,

v1=λ1f1 (2)

• v1 is the speed of the transverse waves formed in a violinist violin,
• λ1 is the wavelength of waves,
• f1 is the frequency of the waves,

Compare equation (1) and (2) to find λ1

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