# Homework Set 9

Many of the questions in this homework set use the speed of sound in air, which depends on the temperature.

$v=331+0.6T \mathrm{ms^{-1}}$

In the above formula $T$ is the temperature in $\mathrm{^{o}C}$

## Problem 15.50

This relates to standing waves on a string. The velocity is obtained from formula $v=\sqrt{\frac{F_{T}}{\mu}}$ and the frequencies are then related to the velocity and the length by the formula $f_{n}=\frac{nv}{2l}$.

## Problem 15.62

You need to decide which harmonics the resonance correspond to, then once you know you can use the same formula from the previous question to find the velocity.

## Problem 15.67

Recall that in refraction $\frac{\sin\theta_{2}}{\sin\theta_{1}}=\frac{v_{2}}{v_{1}}$

## Problem 16.13

Refer to the information on the equation for a traveling wave in lecture 27 and for the relationship between displacement waves and pressure waves in lecture 29.

## Problem 16.25

Intensity is power per unit surface area. Sound level is measured in decibels and is a logarithmic measure of intensity. We hear loudness on a logarithmic scale.

## Problem 16.26

This uses the same concepts as the previous question.

## Problem 16.40

Assume that the sound is being generated by the fundamental mode of a tube open at each end. Consider the boundary conditions at the ends of the tube to determine the relationship between the length of the tube and the wavelength of the sound. You'll need to use the formula for the velocity of sound in air that you can find at the top of the page.

## Problem 16.46

Use the difference between the two frequencies along with the length of the tube to determine the velocity of sound and then the frequency of the fundamental mode.

## Problem 16.57

You should find the standing mode frequency closest to 262Hz in each flute. The difference between the two frequencies is the beat frequency.

## Problem 16.58

Destructive interference will occur when the microphone is $\lambda/2$ more distant from one than the other. How does switching the phase of the two waves affect the condition for constructive and destructive interference.

## Problem 16.60

Use the formula at the beginning of this page for the velocity, find the frequencies and from their difference the beat frequency. What is the wavelength of the wave when beats occur?

## Problem 16.62

This problem corresponds to the double doppler effect when sound bounces off an object and comes back to it's source.

## Problem 16.64

A combined beats and doppler effect problem.