Question

Two waves of the same pitch have amplitude in the ratio 1:3 what will be the ratio of their loudness and pitch​

Answer 1

$\huge\star\:\:{\orange{\underline{\red{\mathbf{Answer}}}}}$

We are familiar with the term loudness and pitch

$\bf\orange{Pitch\::-\:}$

Pitch is the characteristic of sound that tells us whether the sound is shrill or grave . It is measured in Hertz .

$\bf\pink{Loudness\::-\:}$

It is the determined by the amplitude of a sound wave . It is measured in decibels (dB) .

$\huge\blue{\boxed{Answer}}$

Loudness is directly proportional to amplitude square ratio of loudness . i.e

$\implies\:\dfrac{L_1}{L_2}$

$\implies\:\dfrac{{a_1}^2}{{a_2}^2}$

$\implies\:\dfrac{1^2}{3^2}$

$\implies\:\dfrac{1}{9}$

$\implies\:1:9$

$\huge\purple{\boxed{Second\:Case}}$

Frequency of a sound wave has no effect with its amplitude so thus the frequency remains unchanged .

$\dfrac{Pitch\:of\:first\:wave}{Pitch\:of\: second\:wave}$

$\implies\:\dfrac{1}{1}$

$\implies\:1:1$

$\displaystyle\huge\pink{\underline{\underline{Thanks}}}$

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\purple{\text{two waves of the same pitch have amplitude in ratio= 1:3}}$

$\red{\text{NOTE:- PITCH JS MEASURED IN Hertz(Hz), where as,loudness is measured in decibels(dB) }}$

$\large\underline\bold{TO\:FIND,}$

$\sf\large\dashrightarrow ratios\:of\:loudness\:and\:pitch$

$\large\underline\bold{SOLUTION,}$

✯FOR LOUDNESS,

${\text{it is directly proportional to the square of amplitude ratio.}}$

$\sf\therefore L \propto \dfrac{L_1}{L_2}$

$\sf\dashrightarrow L=\bigg( \dfrac{x_1}{x_2} \bigg)^2$

$\sf\implies L= \dfrac{1^2}{3^2}$

$\sf\implies L= \dfrac{1}{9}$

$\sf\implies 1:9$

$\large{\boxed{\bf{ \star\:\: the\: ratio\: of \:there\: loudness \:is \:1:9 dB\:\: \star}}}$

✯FOR PITCH,

$\sf\therefore pitch\: doesn't\:have\:effect\:of\:its\: amplitude$

SO,

$\blue{\text{frequency of pitch remains same}}$

$\sf\therefore two\:waves:- W_1=1,W_2=1$

We get,

PITCH IN RATIO,

$\sf\implies \dfrac{pitch\:of\:wave_1}{pitch\:of\:wave_2}$

$\sf\implies \dfrac{1}{1}$

$\sf\implies 1:1$

$\large{\boxed{\bf{ \star\:\: the\: ratio\: of \:there\: pitch \:is \:1:1 Hz\:\: \star}}}$

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