Skip to main content
Pearson+ LogoPearson+ Logo
Ch 16: Traveling Waves
Back
Previous problem
Next problem
All textbooksKnight Calc 5th EditionCh 16: Traveling WavesProblem 16

Chapter 16, Problem 16

What are the sound intensity levels for sound waves of intensity (a) 3.0 x 10⁻⁶ W/m²?

Verified Solution
Video duration:
2m
This video solution was recommended by our tutors as helpful for the problem above.
382
views
Was this helpful?

Video transcript

Hey, everyone. Welcome back in this problem. We have an experiment conducted by students to calculate the sound intensity level of a sound device in decibels. And as we're asked to determine that sound intensity level, if the students record a sound wave with an intensity of 4. times 10 to the exponent negative six watts per meter squared. We have four answer choices all in decimals. Option A 67 option B negative option C negative 76 option D 76. So we're given the intensity, you wanna find the sound intensity level. Let's recall that we can relate the two through the following equation. The sound intensity level beta, it gonna be equal to 10 decibels multiplied by log base 10 of the intensity I divided by the reference intensity I not. Now we're given I in the problem I not is a constant. OK. We can look that up in a table in our textbook that our professor provided. And so we have everything we need. This is just a matter of substituting in these values. So beta is gonna be equal to 10 decimals multiplied by a log base 10 of 4.5 times 10 to the exponent negative six watts per meter squared, divided by that reference intensity which is 10 to the exponent negative 12 watts per meter squared. OK. The units will divide out inside of that log. If we simplify, this is gonna be equal to 10 decibels multiplied by log base 10 of 4. times 10 to the exponent six. I'm working this out on our calculator gives us 66. decibels. OK. And that is the answer we were looking for. That is the sound intensity level. If we round this to the nearest decibel, we can see that this is gonna correspond with answer choice. A 67 decibels. That's it for this one. Thanks everyone for watching. I hope this video helped.
Previous problemNext problem
Related Practice
Textbook Question
FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string?

517
views
Textbook Question
The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.

335
views
Textbook Question
FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.

503
views
Textbook Question
Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.
334
views
Textbook Question
A sound wave is described by D (y,t) = (0.0200 mm) ✕ sin [(8.96 rad/m)y + (3140 rad/s)t + π/4 rad], where y is in m and t is in s. b. Along which axis is the air oscillating?
393
views
Textbook Question
One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45° to your right. What is the difference in arrival times? Give your answer in microseconds. Hint: You are looking for the difference between two numbers that are nearly the same. What does this near equality imply about the necessary precision during intermediate stages of the calculation?

376
views