   Chapter 14, Problem 51P

Chapter
Section
Textbook Problem

A 60.00-cm guitar string under a tension of 50,000 N has a mass per unit length of 0.100 00 g/cm. What is the highest resonant frequency that can he heard by a person capable of hearing frequencies up to 20 000 Hz?

To determine
The highest resonant frequency can be heard by a person.

Explanation

Given Info: The length of the strength is 60.0 cm, tension under the string is 50.0 N, and mass per unit length is 0.10 g/cm

Formula to calculate the speed of transverse wave in the string is,

v=Tμ

• v is the speed of the waves in the string
• T is the tension in the string and
• μ is the mass per unit length.

Substitute 50.0N for T and 0.10g/cm for μ .

v=(50.0N)(0.10g/cm)(1kg1000g)(100cm1m)=70.7m/s

Calculate the fundamental wavelength.

λ=2L

• L is the length of the string.

Substitute 60.0cm for L.

λ=2(60.0cm)(0.01m1cm)=1.20m

Thus, the fundamental wavelength of the waves is 1.20 m.

Formula to calculate the fundamental frequency is,

f=vλ

• f is the fundamental frequency of the wave

Substitute 70.7 m/s for v and 1.20m for λ .

f=70.7m/s1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 