Physics 208-02 – Introductory Physics II

Solution Set 4

Nazareth College

Department of Chemistry & Biochemistry

Robert F Szalapski, PhD – Adjunct Lecturer

www.CallMeDrRob.com

Spring 2012

## § Chapter 11, Problem 23

At time a mass at rest on the end of a horizontal spring () is struck by a hammer which gives the mass an initial speed of .

### § (a)

Determine the period and frequency of the motion.

### § (b)

Determine the amplitude of the motion.

Initially, immediately after being struck, it is at the equilibrium position, which means the positions of maximum velocity.

### § (c)

Determine the maximum acceleration.

Combine Hooke’s Law, , with Newton’s Second Law, .

We’ll get the largest acceleration when the displacement is a maximum. Taking just the magnitude,

### § (d)

Determine the total energy.

We can compute this using when all of the energy is kinetic, or we can use when all of the energy is potential.

## § Chapter 11, Problem 52

If a violin string vibrates at as its fundamental frequency, what are its first four harmonics?

Use

Then

## § Chapter 11, Problem 53

A violin string vibrates at when unfingered. At what frequency will it vibrate when fingered one-third of the way down the from the end such that the vibrating length is two-thirds of the original length?

## § Chapter 11, Problem 55

The velocity of waves on a string is . If the frequency of standing waves is , how far apart are the adjacent nodes?

The distance between nodes is one-half wavelength, or .

## § Chapter 11, Problem 56

If two successive overtones of a violin are and , what is the frequency of the fundamental?

Use

So

## § Chapter 11, Problem 57

A guitar string is long and has a mass of . The distance from the bridge to the support post is , and the string is under a tension of . What are the frequencies of the fundamental and first two overtones?

## § Chapter 11, Problem 58

A particular guitar string is supposed to vibrate at , but it is measured to vibrate at . By what percent should the tension in the string be changed to correct the frequency?

Write this equation twice realizing that the wavelength and the mass per length do not change.

To compute the percentage change,