第17章音

What is the difference between sound and hearing?

You will learn that light is an electromagnetic wave that can travel through a vacuum. Can sound waves travel through a vacuum?

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

Consider a sound wave moving through the air modeled with the equation$s\left(x,t\right)=6.00\text{nm}$
$\text{cos}\left(54.93{\text{m}}^{\mathrm{-1}}x-18.84\times {10}^3{\text{s}}^{\mathrm{-1}}t\right).$ What is the shortest time required for an air molecule to move between 3.00 nm and –3.00 nm?

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 as $\text{Δ}P=1.80\text{Pa}\text{sin}\left(55.41{\text{m}}^{\mathrm{-1}}x-\mathrm{18,840}{\text{s}}^{\mathrm{-1}}t\right).$ What is the maximum change in pressure, the wavelength, the frequency, and the speed of the sound wave?

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

The displacement of the air molecules in sound wave is modeled with the wave function $s(x,t)=5.00\text{nm}$
$\text{cos}(91.54{\text{m}}^{\mathrm{-1}}x-3.14\times {10}^4{\text{s}}^{\mathrm{-1}}t)$. (a) What is the wave speed of the sound wave? (b) What is the maximum speed of the air molecules as they oscillate in simple harmonic motion? (c) What is the magnitude of the maximum acceleration of the air molecules as they oscillate in simple harmonic motion?

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 $v=340.00\text{m/s}\text{.}$ The sound wave is modeled with the wave function $s\left(x,t\right)=s_{\text{max}}\text{cos}\left(kx-\omega t+\varphi \right).$ 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 is the frequency at which the speaker is oscillating?

A 250-Hz tuning fork is struck and begins to vibrate. A sound-level meter is located 34.00 m away. It takes the sound $\text{Δ}t=0.10\text{s}$ to reach the meter. The maximum displacement of the tuning fork is 1.00 mm. Write a wave function for the sound.

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

Porpoises emit sound waves that they use for navigation. If the wavelength of the sound wave emitted is 4.5 cm, and the speed of sound in the water is $v=1530\text{m/s,}$ what is the period of the sound?

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 $v=343\text{m/s,}$ what is the wavelength of the sound waves?

A bat sends of a sound wave 100 kHz and the sound waves travel through air at a speed of $v=343\text{m/s}\text{.}$ (a) If the maximum pressure difference is 1.30 Pa, what is a wave function that would model the sound wave, assuming the wave is sinusoidal? (Assume the phase shift is zero.) (b) What are the period and wavelength of the sound wave?

Consider the graph shown below of a compression wave. Shown are snapshots of the wave function for $t=0.000\text{s}$ (blue) and $t=0.005\text{s}$ (orange). What are the wavelength, maximum displacement, velocity, and period of the compression wave?

Consider the graph in the preceding problem of a compression wave. Shown are snapshots of the wave function for $t=0.000\text{s}$ (blue) and $t=0.005\text{s}$ (orange). Given that the displacement of the molecule at time $t=0.00\text{s}$ and position $x=0.00\text{m}$ is $s\left(0.00\text{m},0.00\text{s}\right)=1.08\text{mm,}$ derive a wave function to model the compression wave.

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
$v=343\text{m/s,}$ what is the wavelength of the sound wave?