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## Homework Statement

A string has the fundamental tone of

##s_1 = A_1\sin (\omega_1 t - k_1 x)##

Determinate the wave equation for the first harmonic of the string if the sound intensity level of the harmonic is 20dB lower than the fundamental tone. ##\omega_1 = 1360/s## and ##k_1 = 4/m##.

## Homework Equations

Sound intensity level

##L = 10\lg (\frac{I_1}{I_0} )##

Sound intensity is proportional to the wave amplitude squared

##I \sim A^2##

## The Attempt at a Solution

Sound intensity level

##-20 = 10\lg( \frac{I_2}{I_1}) \Longleftrightarrow I_2 = 0.01I_1##

Amplitude relationship

##\frac{A_2}{A_1} = 0.1 \Longleftrightarrow A_2 = 0.1A_1##

The first harmonic got double the frequency so

##s_2 = 0.1A_1 \sin(2 \omega_1 t - 2 k_1 x)##

which is wrong. According to the answer key it should be

##s_2 = 0.05A_1\sin(2 \omega_1 t-2k_1 x)##

Why is it 0.05?