A sound source transfers average power \(0.020\,\mathrm{W}\) through area \(4.0\,\mathrm{m^2}\). Find the intensity.

A sound has intensity \(3.0\times10^{-6}\,\mathrm{W\,m^{-2}}\) crossing area \(12\,\mathrm{m^2}\). Find the average power crossing that area.

A point source radiates \(1.0\,\mathrm{W}\) uniformly. Find the intensity \(2.0\,\mathrm{m}\) away.

Find the sound intensity level for \(I=1.0\times10^{-8}\,\mathrm{W\,m^{-2}}\), using \(I_0=1.0\times10^{-12}\,\mathrm{W\,m^{-2}}\).

A sound level is \(70\,\mathrm{dB}\). Find the intensity using \(I_0=1.0\times10^{-12}\,\mathrm{W\,m^{-2}}\).

A sound intensity is multiplied by \(100\). By how many decibels does the sound level change?

The distance from an ideal point source is doubled. By what factor does the intensity change?

The pressure amplitude of a plane sound wave is doubled while the medium is unchanged. By what factor does the intensity change?

A sound level increases from \(55\,\mathrm{dB}\) to \(75\,\mathrm{dB}\). Find the intensity ratio \(I_2/I_1\).

A \(0.50\,\mathrm{W}\) source radiates uniformly. Find the distance at which the intensity is \(1.0\times10^{-3}\,\mathrm{W\,m^{-2}}\).

For air with \(\rho=1.20\,\mathrm{kg\,m^{-3}}\) and \(v=340\,\mathrm{m\,s^{-1}}\), find the pressure amplitude corresponding to \(I=2.0\times10^{-4}\,\mathrm{W\,m^{-2}}\).

A microphone measures pressure amplitude \(0.30\,\mathrm{Pa}\). Estimate the intensity in air with \(\rho=1.20\,\mathrm{kg\,m^{-3}}\) and \(v=340\,\mathrm{m\,s^{-1}}\).

Two identical incoherent sources each produce intensity \(I\) at a listener. Find the total intensity and the decibel increase relative to one source.

A source has level \(80\,\mathrm{dB}\) at \(5.0\,\mathrm{m}\). Assuming spherical spreading, estimate the level at \(20\,\mathrm{m}\).

A sound source is moved from distance \(r\) to distance \(3r\). Derive the change in sound level in decibels for ideal spherical spreading.

A listener wants to reduce sound level by \(12\,\mathrm{dB}\) by moving farther from an ideal point source. Find the required distance ratio \(r_2/r_1\).

A plane sound wave enters a second medium. Its pressure amplitude is unchanged, but \(\rho v\) is twice as large. Use \(I=(\Delta p_{\max})^2/(2\rho v)\) to determine the intensity ratio and interpret the result.

A point source radiates total power \(P\). Derive the radius at which the sound level is \(\beta\), using reference intensity \(I_0\).

Two coherent equal-amplitude sound waves meet in phase at a point. Compare the resultant pressure amplitude and intensity with one wave alone. Explain why this differs from simply adding intensities of incoherent sources.

A sound level meter reports \(\beta_1\) at distance \(r_1\) from an isotropic source. Derive the source power \(P\) in terms of \(\beta_1\), \(r_1\), and \(I_0\).