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Chapter 19: Problem 13

A sound wave of intensity \(1.60 \mu \mathrm{W} / \mathrm{cm}^{2}\) passes through a surface of area \(4.70 \mathrm{~cm}^{2} .\) How much energy passes through the surface in \(1 \mathrm{~h}\) ?

Short Answer

Expert verified
The amount of energy that passes through the surface in one hour is approximately \(27072 \, Joules\).

Step by step solution

01

Conversion to SI units

First, convert all the values to their respective SI units. 1 hour should be converted to seconds and also convert the intensity from microWatt to Watt. Here, we know \(1 \mathrm{~hour} = 3600 \mathrm{~s}\) and \(1 \mu \mathrm{W} = 10^{-6} \mathrm{W}\). So, the time becomes \(1 \mathrm{~hour} = 3600 \mathrm{~s}\) and intensity becomes \(1.60 \mu \mathrm{W} / \mathrm{cm}^{2} = 1.60 \times 10^{-6} \mathrm{W} / \mathrm{cm}^{2}\).
02

Calculate the total energy

The formula for the energy of wave is given by \(Energy = Intensity \times Area \times Time\). Now we can plug in the numbers and calculate the energy. \(Energy = 1.60 \times 10^{-6} \mathrm{W} / \mathrm{cm}^{2} \times 4.70 \mathrm{~cm}^{2} \times 3600 \mathrm{~s}\). When calculating this, make sure to keep your units straight, and remember cm^2 will cancel out.
03

Simplifying the Result

Simplify the equation and solve for the final energy. The answer will be expressed in Joules since the unit for energy in the International System of Units (SI) is Joules.

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Most popular questions from this chapter

A sound wave in a fluid medium is reflected at a barrier so that a standing wave is formed. The distance between nodes is \(3.84 \mathrm{~cm}\) and the speed of propagation is \(1520 \mathrm{~m} / \mathrm{s}\). Find the frequency.

The A string of a violin is a little too taut. Four beats per second are heard when it is sounded together with a tuning fork that is vibrating accurately at the pitch of concert \(\mathrm{A}(440 \mathrm{~Hz})\). What is the period of the violin string vibration?

A well with vertical sides and water at the bottom resonates at \(7.20 \mathrm{~Hz}\) and at no lower frequency. The air in the well has a density of \(1.21 \mathrm{~kg} / \mathrm{m}^{3}\) and a bulk modulus of \(1.41 \times 10^{5} \mathrm{~Pa}\). How deep is the well?

A person in a car blows a trumpet sounding at \(438 \mathrm{~Hz}\). The car is moving toward a wall at \(19.3 \mathrm{~m} / \mathrm{s} .\) Calculate \((a)\) the frequency of the sound as received at the wall and \((b)\) the frequency of the reflected sound arriving back at the source.

Show that the sound wave intensity \(I\) can be written in terms of the frequency \(f\) and displacement amplitude \(s_{\mathrm{m}}\) in the form $$ I=2 \pi^{2} \rho v f^{2} s_{\mathrm{m}}^{2} $$
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