91影视

Sound levels differ by $\mathrm{尾}=37\text{鈥塪产}$.

We have to use the formula for sound level in terms of intensity to calculate the intensity ratio. To calculate the ratio of pressure amplitudes, we will use the formula for pressure amplitude in terms of displacement amplitude.

Formula:

The scale of sound intensity level,

$\mathbf{螖尾}\mathbf{=}\mathbf{\left(}\mathbf{10}\mathbf{\text{鈥塪叠}}\mathbf{\right)}\mathbf{log}\left(\frac{I_1}{I_2}\right)$ 鈥�(颈)

The ratio of pressure amplitudes,

$\frac{{\mathbf{螖辫}}_{\mathbf{m}\mathbf{1}}}{{\mathbf{螖辫}}_{\mathbf{m}\mathbf{2}}}\mathbf{=}\sqrt{\frac{{\mathbf{I}}_{\mathbf{1}}}{{\mathbf{I}}_{\mathbf{2}}}}$ 鈥�(颈颈)

The ratio of displacement amplitude,

$\frac{{\mathbf{s}}_{\mathbf{m}\mathbf{1}}}{{\mathbf{s}}_{\mathbf{m}\mathbf{2}}}\mathbf{=}\sqrt{\frac{{\mathbf{I}}_{\mathbf{1}}}{{\mathbf{I}}_{\mathbf{2}}}}$ 鈥�(颈颈颈)

We are given the difference in sound levels. We can find intensity ratio by taking antilog on both sides of equation (i) as:

$\begin{array}{c}\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}={10}^{\mathrm{螖尾}/10\text{鈥塪叠}}\\ ={10}^{\frac{37\text{鈥塪叠}}{10\text{鈥塪叠}}}\\ ={10}^{3.7}\\ =5011.872\\ \frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}鈮�5012\end{array}$

Hence, the value of ratio of intensities is $5012$.

Using equation (ii), and the value of intensity ratio, we get the ratio of pressure amplitude as:

$\begin{array}{c}\frac{{\mathrm{螖辫}}_{\mathrm{m}1}}{{\mathrm{螖辫}}_{\mathrm{m}2}}=\sqrt{\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}}\\ =\sqrt{5011.87}\\ =70.79\\ \frac{{\mathrm{螖辫}}_{\mathrm{m}1}}{{\mathrm{螖辫}}_{\mathrm{m}2}}=71\end{array}$

Hence, the value of ratio of pressure amplitude is$71$ .

Using equation (iii) and the value of intensity ratio, we can get the displacement amplitude as:

$\begin{array}{c}\frac{{\mathrm{s}}_{\mathrm{m}1}}{{\mathrm{s}}_{\mathrm{m}2}}=\sqrt{\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}}\\ =\sqrt{5011.87}\\ =70.79\\ \frac{{\mathrm{s}}_{\mathrm{m}1}}{{\mathrm{s}}_{\mathrm{m}2}}鈮�71\end{array}$

Hence, the value of ratio of displacement amplitude is$71$ .