17.1 Sound Waves

What is the difference between sound and hearing?

Sound waves can be modeled as a change in pressure. Why is the change in pressure used and not the actual pressure?

Consider a sound wave modeled with the equation$s \left(x , t\right) = 4.00 \text{nm}$
$\text{cos} \left(3.66 \text{m}^{−1} x - 1256 \text{s}^{−1} t\right) .$ What is the maximum displacement, the wavelength, the frequency, and the speed of the sound wave?

Consider a diagnostic ultrasound of frequency 5.00 MHz that is used to examine an irregularity in soft tissue. (a) What is the wavelength in air of such a sound wave if the speed of sound is 343 m/s? (b) If the speed of sound in tissue is 1800 m/s, what is the wavelength of this wave in tissue?

A sound wave is modeled with the wave function $\Delta P = 1.20 \text{Pa} \text{sin} \left(k x - 6.28 \times 10^{4} \text{s}^{−1} t\right)$ and the sound wave travels in air at a speed of $v = 343.00 \text{m}/\text{s} .$ (a) What is the wave number of the sound wave? (b) What is the value for $\Delta P \left(3.00 \text{m} , 20.00 \text{s}\right)$?

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates at a frequency f, creating a sound wave that moves down the tube. The wave moves through the tube at a speed of $v = 340.00 \text{m}/\text{s} .$ The sound wave is modeled with the wave function $s \left(x , t\right) = s_{\text{max}} \text{cos} \left(k x - \omega t + \phi\right) .$ At time $t = 0.00 \text{s}$, an air molecule at $x = 3.5 \text{m}$ is at the maximum displacement of 7.00 nm. At the same time, another molecule at $x = 3.7 \text{m}$ has a displacement of 3.00 nm. What…

A sound wave produced by an ultrasonic transducer, moving in air, is modeled with the wave equation $s \left(x , t\right) = 4.50 \text{nm} \text{cos} \left(\right. 9.15 \times 10^{4} \text{m}^{−1} x -$
$2 \pi \left(5.00 \text{MHz}\right) t \left.\right) .$ The transducer is to be used in nondestructive testing to test for fractures in steel beams. The speed of sound in the steel beam is $v = 5950 \text{m}/\text{s} .$ Find the wave function for the sound wave in the steel beam.

Bats use sound waves to catch insects. Bats can detect frequencies up to 100 kHz. If the sound waves travel through air at a speed of $v = 343 \text{m}/\text{s},$ what is the wavelength of the sound waves?

A guitar string oscillates at a frequency of 100 Hz and produces a sound wave. (a) What do you think the frequency of the sound wave is that the vibrating string produces? (b) If the speed of the sound wave is
$v = 343 \text{m}/\text{s},$ what is the wavelength of the sound wave?